Design of a Permanent Magnet
Synchronous Generator for a Vertical
Axis Wind Turbine
Nima Madani
Degree project in
Electrical Engineering
Master of Science
Stockholm, Sweden 2011
XR-EE-EME 2011:013
Design of a Permanent Magnet Synchronous
Generator for a Vertical Axis Wind Turbine
NIMA MADANI
Master of Science Thesis in Electrical Machines and Power Electronics
at the School of Electrical Engineering
Royal Institute of Technology
Stockholm, Sweden, June 2011
Supervisor: Dr. Alija Cosic
Examiner: Professor Chandur Sadarangani
XR-EE-EME 2011:013
Abstract
Different types of permanent magnet generators for wind power application have been subject of research during last two decades. In this thesis different topologies of electrical generators have been investigated for
small scale vertical axis wind turbine application. A two stage induction
generator is proposed as a alternative solution with respect to the cost of
such a system. However, a biggest emphasis in the report has been put
on the design of Permanent Magnet Synchronous Generator (PMSG)
suitable for a small scale Vertical Axis Wind Turbine (VAWT)Ṫhe characteristics of PMSG makes it highly compatible for variable speed Wind
Energy Conversion System (WECS) without any pitch mechanism.
Chapters 2 and 3 summarize a thorough literature survey on wind
energy systems and corresponding electrical machines. The principles
of wind aerodynamics is preceded by a review on wind turbine characteristics and challenges with emphasis on VAWT s. Further different
topologies of electrical machines with focus on PMSG s including Permanent Magnet (PM) configurations, different windings and thermal
behavior is presented. In chapter 4 a brief review on an alternative
solution which includes an Induction Generator (IG) for fixed speed
WECS is given.
Next, In chapters 5, 6 and 7, a PMSG is designed and the design is verified by means of Finite Element Method (FEM) analysis and
thermal modeling. Chapter 5 describes an analytical optimisation of a
longitudinal, inner rotor, radial flux, surface mounted PMSG with concentrated winding and natural air cooling system. Cost of active material is chosen as the optimisation criterion. Concepts like "constraints",
"requirements", "parameters" (including material, geometry and winding) and procedure of the design are described here. In chapter 6, a
FEM model of the optimised machine is developed and the results are
illustrated. The iron losses, calculated in this chapter are utilised in
thermal analysis in chapter 7 . Thermal model developed is based on a
lumped parameter circuit . It ensures the safe thermal behavior of the
machine in nominal operation mode.
Keywords: vertical axis wind turbine, permanent magnet machines, permanent magnet generator, Finite Element Method,
fractional concentrated winding
Referat
Olika typer av permanentmagnetgeneratorer för vindkraftapplikation
har varit föremål för forskning under de senaste två decennierna. I denna
rapprt har olika typer av elektriska generatorer undersökts för småskalig
vertikalaxelvindkraftverkstillämpning. Utifrån kostnasdhänsyn för ett
sådant system, en dubbellindad asynkrongenerator föreslås som en allternativ lösning. Emellertid, har den största vikten i raporten lagts på
undersökningen och design av en permanentmagnetsynkrongenerator
för en småskalig vertikalaxelvindkraftverk. Egenskaper hos permanentmagnetsynkrongenerator (PMSG) lämpar sig väldig bra för variabelhastighet vindenergysystem utan pitch mekanismen. I kapitel 2 och 3,
presenteras en grundlig genomförd litteraturstudie på vindkraftsystem
och motsvarande elektriska maskiner. Principerna för vindaerodynamik
föregås av en genomgång på vindturbin egenskaper och utmaningar med
tonvikt på vertikalaxelvinkraftverk. Vidare, presenteras olika topologier
av elektriska maskiner med fokus på permanentmagnetsynkrongeneratorer inklusive permanentmagnet(PM) konfigurationer, olika typer av
lindningar och termiskt beteende. I kapitel 4 ges en kort översikt av en
alternativ lösning, vilken omfattar en dubbellindanasynkmronenerator.
Därefter i kapitel 5, 6 och 7, ges analytisk undersökning och design av en
permanensynkrongenerator, vilken sedan understöds och verifieras med
hjälp av Finita Element Metoden (FEM) och termisk modellering. Kapitel 5 beskriver ett analytiskt optimiserings process av en longitudinell,
inre rotor, radial flödes, permanetmagnetsynkrongenerator med ytmonterade magneter, koncentrerad lindning och en naturlig luftkylning systemet. Kostnadden av aktivt material har valts som ett optimering kriterium. Begrepp som begränsningar", "krav", parametrar"(inklusive material, geometri och lindningar) och arbetsflöde för design är beskrivna
här. I kapitel 6, ges en beskrivning av den utvecklade FEM-modell av
den optimerade maskinen och resultaten presenteras tydligt. Järnförluster beräknade i detta kapitel, utnyttjas vidare i den termiskanalysen i
kapitel 7. Den termiska modellen baseras på punktvis fördelade parameterkretsen. Detta garanterar en säker drift av maskinen vid nominell
last.
Nyckelord: vertikalaxelvindkraftverk, permanentmagnet maskiner,
permanentmagnet generator, Finita Element Metoden, koncentrerad lindning
Acknowledgment
During past seven months I have had the most fascinating time working on this
thesis. So I would like to express my gratitude for the people who made this great
time.
This work has been possible by guidance of my examiner professor Chandur
Sadarangani throughout the entire work. His confidence in me to tackle this task
is highly appreciated. Next appreciation goes to my supervisor Dr. Alija Cosic
who provided me with assistance whenever I needed it. I am grateful of his effort
towards guiding me along the way.
I also feel thankful of my friends and officemates for their friendship. Shafigh
Nategh and I spent a lot of time on our long discussions. Moreover, I had a nice
time with Sergio, Xiaohu, Roberto, Arif,... . EME staff are appreciated for their
help whenever I turned to them: including Peter Lönn, Eva Pettersson, Andreas
Krings, Naveed Malik, ....
I, additionally, would like to express my gratitude towards my parents and siblings. Endless love of my father, who is my hero, and my mother made it possible
for me to bear the distance. I wish the best for my little sister and my brother in
their lives in return of their support during this period. I, moreover, had a great
time in Uppsala with my aunt and my cousins that I will never forget.
Stockholm
Midsummer 2011
Nima Madani
List of Symbols and Abbreviations
List of Symbols
aP M
A
Acu
bs0
bts
Bm
Br0
Br,m
brs
B
bts
B
brr
B
bδ
B
ccu
cF E
cP M
Cb
Cf
Cp
dF E
Di,min
Di,min,f ailure
Di,min,normal
Dm
Dy
E
f
fs
temperature coefficient of remanence flux density of PM material
wind turbine swept area
copper area per slot
stator slot opening
stator tooth width
maximum of airgap flux density
remanence flux density of PM material at 20◦ C
remanence flux density of the magnet at working
temperature
peak fundamental stator yoke flux density
peak fundamental stator teeth flux density
peak fundamental rotor yoke flux density
peak fundamental airgap flux density
cost coefficient for copper
cost coefficient for steel sheet
cost coefficient for PM material
empirical bearing coefficient
empirical friction coefficient
power coefficient (aerodynamic efficiency)
thickness of lamination
generator’s minimum shaft diameter
generator’s minimum shaft diameter in failure
conditions
generator’s minimum shaft diameter in normal
conditions
average diameter of generator’s bearing
generator’s outer diameter
kinetic energy of a fluid mass in wind turbine
frequency
stator slot fill factor
K −1
m2
m2
m
m
T
T
T
T
T
T
T
Euro
kg
Euro
kg
Euro
kg
w.sec
rad.m3
w sec 3
kg .( rad )
−
m
m
m
m
m
m
w.sec
kg
Hz
−
Jb
hrr
hrs
hss
hsw
I
kcoil
kexcess
kh
kj
kkey
kf ailure
knormal
lav
lF E
lm
L
ṁ
Mbend
nn
nr
ns
p
Pbearing
Pmech
Pn
Pwind
Pwindage
Pcu
Pcu−cs
Pcu−ew
PF E
q
Qs
r
R
Rcu
Rth
T
T0
Tn
α
current density
rotor yoke height
stator yoke height
stator slot height
stator slot wedge height
rms value of nominal current
end winding coefficient
Excess loss coefficient
Hysteresis loss coefficient
Stacking factor
correction factor for strength weakening of the
shaft due to the key slot
safety factor under failure conditions
safety factor under normal conditions
average length of half a turn of the winding coil
stator core length
magnet thickness
generator’s airgap cylinder length
mass flow in wind turbine
bending moment acting on generator’s shaft
generator’s base speed
generator’s rated speed
number of turns per slot
number of poles
rotor’s bearing losses
mechanical extracted power from wind turbine
generator’s rated power
available power in wind
rotor’s windage losses
total copper losses
copper losses in coil sides
copper losses in end windings
iron losses calculated in FEM
number of stator slots per pole per phase
number of stator slots
wind turbine’s rotor plane radius
generator’s airgap cylinder radius
phase winding resistance
thermal resistance
temperature
average temperature of ambient
generator’s rated torque
magnet angle
A
m2
m
m
m
m
A
−
w
( T )1.5
m3 sec
w.sec
T 2 m3
−
−
−
−
m
m
m
m
kg
sec
N.m
rpm
rpm
−
−
w
w
w
w
w
w
w
w
w
−
−
m
m
Ω
◦ C/w
◦C
◦C
N.m
electrical◦
αmech
β
βmech
γ
δ
δe
η
ϑ
λ
µr
ρ
ρcu
ρF E
ρP M
σ
σperm
σyield
τs
ω
ωm
geometrical correction factor
blade pitch angle
geometrical correction factor
undercut angle
airgap length
effective airgap length
efficiency
wind velocity
tip speed ratio
relative permeability of the magnet
air mass density
copper resistivity
steel sheet material’s mass density
PM material’s mass density
classical loss coefficient (conductivity)
permissible strength of shaft material
yield strength of shaft material
slot pitch
wind turbine’s rotor tip angular speed
mechanical angular speed of generator’s rotor
List of Abbreviations
AC Alternative Current
BLAC Brushless Alternative Current
DC Direct Current
DFIG Double Fed Induction Generator
DOL Direct Online
EMF Electro-Motive Force
FEM Finite Element Method
HAWT Horizontal Axis Wind Turbines
IEC International Electrotechnical Commission
IG Induction Generator
IPM Interior Permanent Magnet
LCM Least Common Multiple
−
◦
−
◦
m
m
%
m
sec
−
−
kg
m3
Ω.m
kg
m3
kg
m3
1
( Ω.m
)
N
m2
N
m2
m
rad
sec
rad
sec
MMF Magneto-Motive Force
MPPT Maximum Power Point Tracking
PM Permanent Magnet
PMSG Permanent Magnet Synchronous Generator
PMSM Permanent Magnet Synchronous Machine
PWM Pulse Width Modulation
RFPM Radial Flux Permanent Magnet
rpm Rotation Per Minute
rms Root Mean Square
SCIG Squirrel Cage / Short Circuit Induction Generator
SCIM Squirrel Cage / Short Circuit Induction Machine
SG Synchronous Generator
SMPM Surface Mounted Permanent Magnet
VAWT Vertical Axis Wind Turbine
WECS Wind Energy Conversion System
WRIG Wounded Rotor Induction Generator
WRIM Wounded Rotor Induction Machine
WRSG Wounded Rotor Synchronous Generator
Contents
Contents
1 Introduction
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Wind Energy Systems
2.1 Wind Turbine Aerodynamics . . . . . . . . . .
2.2 Wind Turbines . . . . . . . . . . . . . . . . . .
2.2.1 Working Principle of VAWT . . . . . .
2.3 Mechanical Drive Train . . . . . . . . . . . . .
2.3.1 Fixed Speed or Variable Speed . . . . .
2.3.2 Geared or Direct Driven . . . . . . . . .
2.4 Operation Sequence and Control . . . . . . . .
2.4.1 Operation Sequence . . . . . . . . . . .
2.4.2 Control . . . . . . . . . . . . . . . . . .
2.5 Comparison Between VAWTs and HAWTs . . .
2.5.1 Design: Yaw Mechanism . . . . . . . . .
2.5.2 Design: Axis of Direction . . . . . . . .
2.5.3 Design: Direct Drive . . . . . . . . . . .
2.5.4 Design: Wind turbine construction . . .
2.5.5 Design: Structural Mechanics . . . . . .
2.5.6 Aerodynamics: Performance . . . . . . .
2.5.7 Aerodynamics: Power Control . . . . . .
2.5.8 Noise . . . . . . . . . . . . . . . . . . .
2.6 Vibrations in Wind Energy Systems . . . . . .
2.6.1 Torsional Vibrations of the Drive Train
2.7 Noise Emission . . . . . . . . . . . . . . . . . .
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3 Electrical Machines for Wind Energy Systems
3.1 Different Topologies of Electrical Machines . . . . . . . . . . . . . .
3.1.1 DC Generators . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 FEM Simulation of PMSG
6.1 Initial Considerations . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Results of FEM Simulations . . . . . . . . . . . . . . . . . . . . . . .
6.3 Iron Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.2
3.3
3.4
3.5
3.1.2 Induction Generators . . . . . . . . . . . . .
3.1.3 Synchronous Generators . . . . . . . . . . .
PM Synchronous Machines . . . . . . . . . . . . .
3.2.1 Radial Flux or Axial Flux . . . . . . . . . .
3.2.2 Longitudinal or Transversal . . . . . . . . .
3.2.3 Inner Rotor or Outer Rotor . . . . . . . . .
PM Configurations . . . . . . . . . . . . . . . . . .
3.3.1 Surface Mounted Magnets . . . . . . . . . .
3.3.2 Inset Magnets . . . . . . . . . . . . . . . . .
3.3.3 Buried Magnets . . . . . . . . . . . . . . . .
Winding . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Distributed Winding . . . . . . . . . . . . .
3.4.2 Concentrated Winding . . . . . . . . . . . .
3.4.3 Single Layer Concentrated Non-Overlapping
Thermal Behaviour . . . . . . . . . . . . . . . . . .
3.5.1 Consequences of Temperature Rise . . . . .
3.5.2 Cooling System . . . . . . . . . . . . . . . .
3.5.3 Heat Transfer Theory . . . . . . . . . . . .
3.5.4 Losses in PMSG . . . . . . . . . . . . . . .
4 Induction Generator
4.1 Fixed Speed Induction Generator . . . . . .
4.2 Selection of Induction Motor as Generator .
4.2.1 Temperature Rise . . . . . . . . . .
4.2.2 Efficiency . . . . . . . . . . . . . . .
4.2.3 Size . . . . . . . . . . . . . . . . . .
4.3 Two Step Fixed Speed Induction Generator
4.4 Self Excited Induction Generator . . . . . .
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5 Analytical Design of PMSG
5.1 Design Requirements and Constraints . . . . .
5.1.1 Mechanical Calculation: Minimum Shaft
5.2 Design Parameters . . . . . . . . . . . . . . . .
5.2.1 Material . . . . . . . . . . . . . . . . . .
5.2.2 Geometry . . . . . . . . . . . . . . . . .
5.2.3 Temperature . . . . . . . . . . . . . . .
5.2.4 Winding (Concentrated) . . . . . . . . .
5.3 Design Procedure . . . . . . . . . . . . . . . . .
5.4 Design Objective . . . . . . . . . . . . . . . . .
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7 Thermal Modeling of PMSG
7.1 Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Conclusions and Further Work
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A Datasheet of M400 50A by Surahammar Bruk AB
77
Bibliography
79
List of Tables
82
List of Figures
83
Chapter 1
Introduction
1.1
Background
Energy demands of the modern society has made the way open to invest great
amount of technological effort and capital to renewable energies. Figure 1.1 shows
the amount of annual capital investment in new renewable energies (excluding large
scale hydro power, traditional biomass) between 2004 and 2009. The values include
energy converted into electricity and heat.
Wind energy is one of the renewable energies which has attracted a lot of interest in recent years. By end of 2009, the capacity of wind energy power plants
has reached 158 gigga watts worldwide. The interest in producing electricity puts
certain demands on the electrical machines and drives. Mechanical energy from re-
Figure 1.1. Annual capital investment in new renewable energies between 2004 and
2009 in US Dollars [1].
1
CHAPTER 1. INTRODUCTION
Figure 1.2. Renewable energy share of global energy consumption by 2008 [1].
newables injected to electrical machines is not controllable. This challenge has led
to many technological advancements in induction machines and permanent magnet
synchronous generators. The author, however,would like to emphasize that there is
a great room for growth in renewable energies 1 . So far wind energy contributes to
0.3 % of global energy consumption.
1.2
Objective
Main objective of this thesis is to design a suitable permanent magnet synchronous generator working with a vertical axis wind turbine. Wind energy conversion system consisting of above mentioned elements works on a variable speed
principle. In small scale wind turbines, blade pitch mechanism usually is not applied.
Instead, a power electronics converter compensate variation for the wind variation
and thus it contributes to high power coefficient. The corresponding topology of
PMSG is a surface mounted machine with concentrated winding. This type of
winding suits for low speed applications since implementing high number of poles
is easy. The major benefit of high pole numbers is eradication of gearboxes. Gearboxes result in lower availability of the entire system and they cause high amount of
non-user friendly audible noise. Reduction of magnetic noise by the machine is targeted at the design stage. Additionally, the chosen topology can be easily scaled by
increasing the length of the machine. Of paramount, at the design stage, objective
function is to reduce manufacturing expenses and cost of active material.
1.3
Contents
This section describes the contents of each chapter.
1
see Figure 1.2.
2
1.3. CONTENTS
• Chapter 2 gives an in depth knowledge of wind energy concepts and terminology for electrical designer. The emphasis is on VAWT.
• Chapter 3 reviews the principles of rotating electrical machines for wind speed
application. The emphasis is on PMSG.
• Chapter 4 offers an alternative option for PMSG.
• Chapter 5 illustrates analytical design stage with optimisation.
• Chapter 6 verifies the optimised PMSG with the help of FEM analysis.
• Chapter 7 investigates thermal behavior of the optimised machine.
• Chapter 8 clinches the work, conclusions and further suggested work are given
here.
3
Chapter 2
Wind Energy Systems
Wind energy systems have been subject of research for decades. They consist
of wind turbines and electrical generators. The first section covers the basics of
VAWT . Initially in this section, aerodynamics of wind turbines are presented.
Subjects like control, dynamic vibration and noise emission in VAWT are covered.
Furthermore, a separate section is dedicated to a comparison between Horizontal
Axis Wind Turbines (HAWT) and VAWT .
The role of a wind energy system is to capture mechanical energy in the airflow
and convert it to electrical energy. Usually it consists of a wind turbine rotor, for the
former purpose, and an electrical machine working as generator for the latter. The
variation in the wind speed is one of the factors that affects the specifications of wind
energy systems. In other words design of the wind systems’ components demands
special consideration. The amount of accessible mechanical energy depends on the
size of the wind turbine and the wind regime of the site.
2.1
Wind Turbine Aerodynamics
The amount of the kinetic energy in the air flow can be determined based on
the size of wind turbine and the wind speed. The elementary momentum theory
gives an explaination of energy conversion in ideal circumstances. The amount of
the kinetic energy of a fluid mass ṁ with a mass density ρ , moving at a velocity ϑ
through the area A is
1
(2.1)
E = · ṁ · ϑ2
2
and the mass flow is
ṁ = A · ρ · ϑ
(2.2)
The power available in the wind is equal to the amount of energy yield passing per
second.
1
Pwind = E · ṁ = · ρ · A · ϑ3
(2.3)
2
It is obvious that a small variation in the wind speed influences the available
wind power drastically. It was first in 1922, the German engineer Betz showed that
5
CHAPTER 2. WIND ENERGY SYSTEMS
Figure 2.1. Power coefficient versus tip speed ratio [3].
the amount of extractable energy from an air stream is limited. It was shown that,
in a free air stream, the maximum energy is extracted if the wind speed is reduced
by three times far behind the turbine in comparison to in front of it. The maximum
extractable power becomes then, 16/27 of available wind power [2].
For steady state analysis of aerodynamic conversion, a power coefficient diagram
is used. As mentioned, it is not possible to capture all the power in the air flow as
this would result in air standstill immediately after the wind turbine. Aerodynamic
efficiency represents a ratio of captured power and available wind power. In wind
power terminology, it is more known as the power coefficient. Betz factor is the
maximum value for the power coefficient.
The power coefficient Cp is a function of the tip speed ratio λ and the blade
pitch angle β. Equation 2.3 above, is modified according to equation 2.4.
Pmech = Cp .Pwind =
1
· ρ · A · Cp (λ, β) · ϑ3
2
where
(2.4)
r·ω
(2.5)
ϑ
ω is the rotor tip angular speed and r is the rotor plane radius. Blade pitching
means that the rotor blades are rotated along their axis, in order to control the
amount of the absorbed power. 1 In wind turbines which are not equipped with
the control of the blade pitch, power coefficient is merely function of the tip speed
ratio. Figure 2.1 shows a typical power coefficient diagram. Power coefficient is
maximum at the optimum tip speed ratio i.e. in order to capture the maximum
energy, the wind turbine rotor has to be run at this ratio. When the wind turbine
rotor is run at other tip speed ratios, eddies will develop at the blade tip. This
phenomenon reduces the captured energy and it is called stall. It explains the drop
of the power coefficient at other tip speed ratios.
λ=
1
see section 2.4.2
6
2.2. WIND TURBINES
It can be observed from the power coefficient diagram in Figure 2.1, that the
wind turbine is not self starting. For low values of the tip speed ratio, the value of
the power coefficient is negative. Many lift based wind turbines require a minimum
tip speed ratio before they can start to absorb the power [4]. Accordingly, in order
to start up the wind turbine rotor, energy has to be supplied. There are different
ways to do so, one is to utilise an auxiliary self starting turbine like for example
Savonious wind turbine. Another is certain modification in the design of the wind
turbine. Furthermore, electrical starting of wind turbine is yet another possibility.
The generator is, then, fed by the grid for a short duration of time and works as
a motor in order to start the wind turbine. In this solution the wind power plant
cannot operate as a stand alone unit.
2.2
Wind Turbines
Wind turbines are categorised based on two different criteria; First due to their
aerodynamic function; second based on their design.
Considering the aerodynamic performance, wind turbines are divided into drag
based and lift based. The rotors which utilise the drag force of the wind are recognised as low speed turbines. However, in some turbines, the possibility of employing
the lift force is also provided. The lift based turbines are recognised as high speed
rotors. These are capable of capturing higher amount of the wind power compared
to their drag based counterparts and therefore they are the most common solution
today.
Due to the second criterion, wind turbines are classified based on their axis
of rotation. It is more common to distinguish wind systems as HAWT or VAWT.
HAWT s have benefited from technological advancements in the aircraft engineering
because of the blades’ propeller like design. For instance, to achieve more lift forces,
blade shapes’ optimisation are proposed and applied. Power coefficients up to 0.5
of HAWT s have been reported. Today’s VAWT s have reached power coefficient
up to 0.4 at maximum. Figure 2.2 and Figure 2.3 show a H rotor VAWT and an
installed HAWT respectively. Simplicity of the design of the VAWT s is beneficial,
especially the possibility to accommodate some of the drive train components on
the ground together with absence of the yaw system 2 . Some disadvantages of the
system are the lower optimum tip speed ratio, inability to self start and inability to
implement blade pitching for power control purposes. In some of the researchers’
opinion the VAWTś power coefficient can exceed that of HAWT s’ . A comparison
between HAWT s and VAWT s is presented in section 2.5.
2.2.1
Working Principle of VAWT
Figure 2.4 shows a horizontal plan of a VAWT . The hub is assumed to be
located at the centre of the coordinate system. The area with a positive value on
2
see section 2.3 and section 2.5.1
7
CHAPTER 2. WIND ENERGY SYSTEMS
Figure 2.2. An H rotor VAWT [3].
y-axis in Cartesian coordinate system is defined as upwind region and the remaining
area is defined as the downwind region. The angle of attack is the relative angle
between the chord line of the blade cross section and the wind direction. This
angle, seen by the blades in the upwind region, is negative. Since the angle of
attack is negative, the lift force vectors produced on the blade section will point
inwards the rotor. The force can be decomposed into two different components, a
tangential and a normal. The former is along the tangent of the blade and the latter
is perpendicular to the blade.
Moreover, the lift force will be created in downwind region. Here the angle of
attack is positive, the consequent lift force vectors will point outwards the rotor.
Tangential lift forces, originated from upwind and downwind regions, contribute to
the torque production in the rotor. The normal forces lead to thrust along the wind
direction.
8
2.2. WIND TURBINES
Figure 2.3. A 450 kw HAWT with 37 m rotor diameter (Bonus) [2].
Figure 2.4. Horizontal plan of a VAWT [5].
9
CHAPTER 2. WIND ENERGY SYSTEMS
2.3
Mechanical Drive Train
The term "mechanical drive train" stands for all rotating parts of the wind system
from the rotor hub to the rotor of the generator. In conventional power plant technology, two requirements by mechanical drive are met: First equity of input power
to the generator with the amount of needed power by the load; Second matching the
speed levels of the prime mover with the speed of the generator. In wind systems,
however, mechanical drive train does not meet neither of these requirements. The
power production depends on the available wind resource which is not controllable.
Furthermore, wind speed is far from rated speed of the conventional generators.
The drive trains are classified according to implementation of a wind system in
order to compare their characteristics. Each drive type possesses specific advantages
and disadvantages, such as aerodynamic and dynamic performance, controllability,
reliability, maintenance , etc.
2.3.1
Fixed Speed or Variable Speed
In fixed speed wind systems, the rotor speed is determined by the grid frequency
and its variation is limited to around ±1% of the nominal speed. Usually, the
fixed speed wind systems is designed in such a way that it has its optimum wind
speed equal to site mean wind speed. No means for power control is applied and
the advantage is simplicity of operation. Disadvantages are low efficiency of wind
energy system in other wind conditions aside from the mean wind speed, and severe
dynamics performance. Since no control method is implemented, any fluctuations
of power i.e. disturbances in the grid and/or turbulence in the wind, are passed
through the system without any damping. This reduces the quality of the delivered
power to the grid and also causes mechanical stress on the wind turbine rotor. Weak
power systems are sensitive to low power quality delivered by such wind systems.
The efficiency of electrical machines varies with varying electrical load conditions. Therefore most of the fixed speed wind energy systems are designed in a way
to provide the generator with high load. This can be achieved by means of two
generators with different ratings. Another solution is to have two windings with
different pole numbers in the same generator.
In Variable Speed wind systems, power electronics converters keeps the rotor
speed and the grid frequency apart. Therefore it is possible to vary the rotor
speed independent of the grid frequency. Hence, the variation in the input power
will result in the rotor speed variation. The output power from wind system will
be slightly lower than the input power which results in more stable and smooth
delivered power to the grid. The power quality of these wind energy systems is
much better compared to their fixed speed counterparts. Furthermore, they have
lower noise in low wind conditions [6]. In variable speed systems, the wind turbine
is operated in a wider speed range, keeping the tip speed ratio at the optimum. The
advantage is higher energy capture, however, the disadvantage is more complicated
control method [7].
10
2.4. OPERATION SEQUENCE AND CONTROL
2.3.2
Geared or Direct Driven
Wind energy systems can be distinguished based on whether or not they include gearboxes. Wind turbine rotors are capable of rotating at tens of rotations
per minute. However, the conventional electrical machines runs at much higher
speeds e.g. hundreds of Rotation Per Minute (rpm) . The role of a gearbox is to
transfer mechanical energy from low speed to high speed; A step up gearbox is used
then. Implementation of a gearbox has its own disadvantages, e.g. maintenance,
installation complication, cost of equipment, audible noise and losses. The gearbox
is one of the reasons for audible noise in wind energy systems. The losses in the
gearbox are comparable to the losses in the electric machine. Newly designed wind
systems are usually adapted for gearless operation. This solution has become more
reliable, more efficient and less noisy. The main disadvantage is a need for a special
designed generator which tends to be bulky.
Due to the possibility of employing power electronics converters, gearless, or
in other words, direct driven systems can suite for variable speed applications [8].
Converters offer the possibility to operate the generator at low speeds. Although
the converters are source of losses, controllability is a huge advantage compared to
the gearboxes.
Knowledge about construction and operation of gearboxes alleviates their aftermath. Gearboxes are divided into two different configurations; Parallel shaft or spur
gear which has a simpler mechanical construction and a gear ratio of up to 1 : 5
in each stage; Planetary or helical gearbox which has more complicated mechanical
construction and a gear ratio of up to 1 : 12 in each stage. HAWT s run typically
at 20rpm and usually requires more than one stage. Tooth flank friction and oil
flow are the origins of power losses in the gearboxes. The average amount of losses
depends on the gear ratio and the type of the gear. It is estimated as approximately 2% of full power per stage for parallel shaft gears and as 1% of full power
per stage for planetary gears. In practice precise dimensioning of gearbox is of
importance. Otherwise maintenance and operation will experience many problems
and the lifetime will be affected.
2.4
2.4.1
Operation Sequence and Control
Operation Sequence
Operation sequence of the wind turbine is determined by means of three threshold points.
• Cut in velocity ϑCI which is the wind speed the wind turbine starts to deliver
output power. For instance, in VAWT s captured power for low wind speeds
is negative, and the cut in velocity has to be chosen at values greater than the
wind speed at which power coefficient becomes positive.
11
CHAPTER 2. WIND ENERGY SYSTEMS
• The rated wind velocity ϑR is the wind speed at which the captured power
reaches the generator rated power.
• The cut out velocity ϑCO is the highest wind speed at which the wind energy
system is able to operate mechanically safe. Typically this is less than 25 m/s
.
As a result, operation sequence of a wind turbine is divided into, at least, four
regions.
• Region 1, at which the wind speed is less than the cut in speed. In this region,
captured power does not suffice to compensate the internal consumption and
losses. Hence the turbine is parked and is not run.
• Region 2, at which the wind speed is between the cut in speed and the rated
speed. It is sometimes called sub-rated region and the wind turbine is controlled using Maximum Power Point Tracking (MPPT) in order to achieve the
optimum tip speed ratio. MPPT is introduced thoroughly in subsection 2.4.2
.
• Region 3, at which the wind speed is between rated speed and cut out speed.
In this region, there are various control options, namely constant rotor speed,
constant rotor torque and constant rotor power. The first two, comes with the
risk of torque and current overload and they need additional control measures
for overload protection. In the latter two, the speed does not reach to the
rated speed, therefore constant rotor power is proposed [9] .
• Region 4, at which the wind speed exceeds the cut out speed and the wind
turbine is shut down.
2.4.2
Control
The purpose of the control is:
• Limiting the torque and the power experienced by the drive train in order to
increase lifetime.
• Maximising the energy yield for various conditions.
Drive train suffers from fatigue caused by aerodynamic and structural loads. The
structural strength of the wind turbine can be maintained up to a certain wind
speed. In addition, another limiting factor is the rated power of the generator. The
rated power of the generator is reached at rated wind speed of the turbine.
Energy yield depends on the available wind power of the site as well as power
capture by the wind turbine. The energy available in the wind is uncontrollable
since it depends on the wind regime of the site. However, the power capture by the
wind turbine can be maximised by the control method.
There are four different ways to influence the rotor captured power and the
turbine loads. They are:
12
2.4. OPERATION SEQUENCE AND CONTROL
• Angle of attack (blade pitching)
• Flow velocity (variable speed rotor)
• Blade size (variable blade length)
• Blade section aerodynamics
The first two methods are implemented in most of all modern HAWT s and the
work principle behind the control of the power coefficient. They are introduced in
the following subsections.
The working principle behind the variable diameter blade is the control of the
swept area that is useful for minimising the load during high wind speeds. Control
of blade section aerodynamics is implemented by means of active flow control. This
state of the art method is growing rapidly and has the potential to be implemented
on large scale HAWT s [10] .
Generally, control can be implemented in either active or passive way, depending
on utilisation of external energy. Yaw mechanism, blade pitching and variable speed
rotors are examples of contemporary active control methods.
Blade Pitching
In a conventional control method of HAWTs the pitch angle of the rotor blade
is changed mechanically. Blade pitching means that the blades are turned along
their longitudinal axis with the help of an active mechanical device. In this way,
the angle of attack and thereby also the absorbed power varies. The angle of attack
can be changed in two different ways either by decreasing or increasing it. Both
cases reduce the captured power, provided that the angle of attack is in a condition
where the power coefficient is at the maximum. The former requires higher blade
pitching for the same difference in the power coefficient. Hence, the output power
is controlled more precisely.
Fixed-speed-fixed-blade VAWTs suffer from high demands on the self stall regulation property. Usually, small scale VAWT s are not equipped with the blade
pitching control for simplicity reasons. In fixed blade VAWTs, at which the rotor
speed is kept constant, the more the wind speed increases, the larger the angle of
attack becomes. Thus the amount of stall will increase as well. In fixed speed
wind systems, which are connected to the grid directly, the rotor speed is constant
and accordingly the self regulatory stall is always present. From the wind system
components’ point of view, there are several demand points which are listed below.
• Aerodynamic load will be large. Therefore the stiffness and mechanical strength
of the turbine has to be high.
• Overload capacity of the generator has to be high.
• Either the wind turbine rotor should have high starting torque or additional
measures for starting should be provided. This is because self starting by
means of pitching the blades is not provided.
13
CHAPTER 2. WIND ENERGY SYSTEMS
As a result, application of fixed blade VAWTs with variable speed wind systems
rather than with the fixed speed systems are proposed.
The VAWTs’ power coefficient’s optimum is transferred to the lower tip speed
ratios compared to HAWTs’, which according to E. Hau, is their major disadvantage.
As the speed of the VAWT is lower, in order to achieve the same power, VAWTs
require higher torque rate. This might increase the stiffness requirements on VAWT
s [2] .
Maximum Power Point Tracking
The maximum Power Point Tracking is a control method which controls the
wind turbine rotor speed by controlling torque of the generator. The blade pitching
drive is a mechanical equipment which has a delay in response time in rapidly
changing wind conditions. Thus in gusty and turbulent winds, it can influence the
energy yield and subsequently causes mechanical stress on the turbine. However,
in order to maximise the power production, the rotor speed of the generator can be
controlled electrically. MPPT techniques, accordingly, are developed in an attempt
to achieve the maximum power coefficient. This is usually done by adapting the
rotor speed to the optimum tip speed ratio. Rotor speed of an electrical machine
can be controlled by means of the difference in its input power and output power.
The output power of the generator, in a variable speed wind system is controlled
with the help of a power electronics converter. If the speed of the rotor needs to be
increased, the output power is kept lower than captured power. On the other hand,
when the rotor deceleration is required, the output electric power is maintained
higher compared with the captured power.
There are different ways of making the wind speed reference for MPPT . The
simplest one is to measure the wind speed by anemometers that is send it to the
controller. However, there are several issues associated with the wind speed measurement. Generally, measuring the wind speed at a distant place in a large wind
system comes with a certain time delay. In small VAWT s, anemometers, which are
installed nearby are provided. However, lack of quick response time can be influential on reliability, since small VAWT s are usually installed in areas with turbulent
winds.
Sensorless MPPT method is a control method without the wind speed measurement. There are several different approaches for implementation of of such control
method such as constant output power, fixed voltage and the wind speed prediction.
Usually, autoregressive statistical models are used for prediction of the wind speed,
based on the historical data [11]. Captured energy from each set of data is used
for predicting the wind speed at the next time frame. The accuracy of the wind
speed prediction depends on many factors including the length of the sampling time
frame. The shorter the sampling time frame, the higher the accuracy of wind speed
prediction.
One of the major considerations when selecting control method is its easy implementation. Short computation time and low sensitivity to parameter adjustment
14
2.5. COMPARISON BETWEEN VAWTS AND HAWTS
is a benefit.
2.5
Comparison Between VAWTs and HAWTs
A comparison between VAWTs and HAWTs is presented below, both in terms
of design and performance aspects [8]. Furthermore, detailed description is given
for some aspects mentioned earlier in the text
2.5.1
Design: Yaw Mechanism
Unlike the VAWTs , the HAWTs are in need of a yaw mechanism. The function
of yaw mechanism is to direct the rotor in the wind direction in order to maximise
the aerodynamic efficiency. It includes an electrical motor as a drive mechanism and
a control system, which detects the wind direction and command the mechanism
to rotate. The main disadvantages are need for maintenance and the cost of the
equipment, installation and operation. Additionally, there is a delay in rotation
of of the nacelle in the right direction due to the time response. VAWTs, on the
other hand, do not need yaw mechanism, while they are omnidirectional and they
can rotate in both directions. This property makes VAWT s highly suitable for
locations where the wind is gusty or turbulent like mountainous areas and urban
neighborhoods.
2.5.2
Design: Axis of Direction
Some advantages and considerations for VAWT s come with vertical axis of
rotation. Usually, HAWTs’ drive train is located in nacelle on top of the tower.
This increases mechanical stress on the tower, which requires strong foundation. In
VAWTs, a part of the drive train i.e. the generator and the control equipment can
be located on the ground. The mechanical power is transferred via a long shaft
from the hub to the generator, which has many advantages. The generator size and
weight will have low priority as a design constraint. However, torsional vibrations
of the long shaft with high torque might become a problem. A long airgap might be
a remedy. The disadvantage of this is that it might influence the machine design,
which makes the machine costly. A dynamic analysis is proposed.
2.5.3
Design: Direct Drive
VAWTs are more suitable for direct drive applications compared with the HAWTs.
Electric machine in direct drive wind system usually operates with low speed and
high torque. For a constant power rating and constant torque density of a machine,
weight is positively correlated with the torque rating. Consequently design with
higher torque in direct drive will have more weight. In HAWT s higher weight
of the machine in direct drive puts more mechanical stress on the tower. Unlike
HAWTs, this is not an issue for a VAWT, as the machine is located on the ground.
15
CHAPTER 2. WIND ENERGY SYSTEMS
2.5.4
Design: Wind turbine construction
Construction of the blades for VAWTs is easier compared with that of HAWTs
[3]. One reason is that the blades of a HAWT are supported at their root by
connection to the hub and they have to be stiff and self-supportive. Furthermore,
they are twisted along their length for aerodynamical purposes, i.e. to increase
the power capture. This makes the mechanical construction of blades tougher. On
the other hand VAWT s’ blades are connected to the hub in their middle point.
Additionally, the VAWT s’ blades are straight and not twisted along their length,
which makes manufacturing of the blades much easier.
2.5.5
Design: Structural Mechanics
HAWT s and VAWT s are both subject to different mechanical stresses. The
blades of HAWT suffer from cyclic reversing gravity loads as well as periodical loads
due to wind shear. Meanwhile, the blades of VAWT s are associated with bending
moments caused by centripetal acceleration. Torque ripple is generally higher in
VAWTs compared with HAWTs. This alleviates, in variable speed applications,
with higher number of blades and higher size of the wind turbine rotor.
2.5.6
Aerodynamics: Performance
Aerodynamic efficiency of commercialised HAWT s is higher compared with their
VAWT counterparts. A measure for this is the power coefficient, which typically for
HAWT is between 0.4 and 0.5, while for VAWT this is typically 0.4 . HAWTs have
been subject of research for decades and the design optimisation has progressed.
It seems that development of wind power plant technology, with more emphasis
on HAWT, has made it possible to reach higher values of the power coefficient.
HAWTs can start at low wind speeds; On the other hand, VAWTs have poor starting
characteristics and they require to be started by other means.
2.5.7
Aerodynamics: Power Control
HAWT and VAWT can use different methods to control the power flow. Power
control is a necessity otherwise wind turbine rotors might be damaged mechanically
in high wind speeds e.g. 25 m/s . Unlike HAWTs which use blade pitching for
power control, the small VAWT s use electrical machine to control the absorbed
power, since implementation of blade pitching does not suit their scale. The difference between the input power and the output power from the generator can either
accelerate or decelerate the wind turbine rotor speed.
2.5.8
Noise
VAWTs have lower noise compared with that of HAWTs [3]. There are two different sources of noise; First is aerodynamic noise generated by the blades; Second,
16
2.6. VIBRATIONS IN WIND ENERGY SYSTEMS
the mechanical noise generated from the drive train. In general, VAWTs have lower
aerodynamic noise which is strongly related to the wind turbine rotor speed. In
wind systems with power control, rotor speeds are controlled by the optimum tip
speed ratio. HAWTs’ optimum tip speed ratio value is typically between 5 and 7
while it is 4 for VAWTs.
2.6
Vibrations in Wind Energy Systems
Wind systems are prone to vibrations because of slender and elastic construction.
Cyclically alternating forces can be origins of excitation of vibrations and possible
resonances, which can lead to vibration of either one component or entire wind
system. Therefore, in the design stages the vibrational modes of entire wind system
and its subsystems have to be analysed in order to assure dynamic stability. Main
dynamic vibrational behaviours are:
• Aeroelastic instability of the rotor blades.
• Torsional vibrations of the drive train.
• Dynamics of yaw system (limited to HAWT s).
• Vibration of the entire wind turbine.
2.6.1
Torsional Vibrations of the Drive Train
The frequency response of the system is a major criterion to determine the
dynamics of its vibrations and it gives information about all natural frequencies.
Natural frequency is called eigen frequency in the subject of dynamics. Since resonance might occur in the natural frequencies, they are sometimes also referred as
resonant frequency. Therefore, it has to be ensured that natural frequencies of the
system or of its components are far from the applied excitation frequencies, during
the design stage.
Dynamics of the mechanical drive train of the wind systems is influenced by
forced torsional vibrations. The vibrations depend on different characteristics of
participating masses, namely
• Mass moment of inertia.
• Damping constant.
• Rotational stiffness.
Depending on the number of degrees of freedom, the system has one or more eigen
frequencies. In a drive train modeled with one degree of freedom, value of damping
ratio is proportional to the damping constant and inversely proportional to the mass
moment of inertia and the eigen frequency. The damping ratio determines amount
of damping the system intrinsically has. When, in systems with low damping,
17
CHAPTER 2. WIND ENERGY SYSTEMS
resonance occurs, amount of angular displacement might be dramatic that leads to
fatigue or fracture.
A dynamic analysis of mechanical drive train components is proposed. Dynamics
of drive train’s components i.e. electrical machine, shaft and gearbox influence
torsional vibrations of each other and also the drive train entirely. In [12], the
vibration of electromagnetic origin is presented for PMSG s, and essential vibration
modes with shape of possible deflections are distinguished. The gearbox, in geared
system, affects the damping of the system severely. A complete dynamic study is
out of scope of this work. However, the author emphasizes that this study is vital
to guarantee a noise free performance and an acceptable lifetime.
2.7
Noise Emission
Wind system noise emission is of significance especially in populated areas. In
the field of acoustics, it is measured by sound pressure level in dB(A). The acceptable noise level is subject of technical design specifications, standards and legislations. However, for small scale wind systems, its main significance is in customer
satisfaction. The amount of acceptable sound pressure level is legislated, based on
the time (day/night) and surrounding type (variation from fully residential to fully
industrial). Generally, amount of accepted sound pressure level in industrial surroundings is higher compared with the residential surroundings. It is also higher
for days than nights.
Aerodynamic noise of wind systems is less problematic as the wind speed increases. High wind speed contributes to ambient noise, when the wind collides with
obstacles,but it also contributes to high aerodynamic noise of the wind system.
However, on a lower scale it increases 2.5 dB(A) per 1 m/s increase in the wind
speed, where on the other hand wind turbine noise increases only 1.0 dB(A) per 1
m/s increase in the wind speed. In low wind speeds, wind turbine noise is higher
compared with the ambient noise. As the wind speed increases, the ambient noise
starts to exceeds the wind turbine noise. When discrepancy of these noises reaches
to 6 dB(A), then the wind turbine noise is no longer contributing to perceptible
increase in sound pressure level. Generally speaking, at wind speeds higher than 10
m/s, wind turbine aerodynamic noise cannot be perceived.
18
Chapter 3
Electrical Machines for Wind Energy
Systems
3.1
Different Topologies of Electrical Machines
This chapter deals with different topologies of electrical machines for VAWT.
In the text, Direct Current (DC) and induction generators precede synchronous
generators. This chapter, furthermore, discusses "Design of a Permanent Magnet
Synchronous Generator for a Vertical Axis Wind Turbine". Therefore the emphasis
is put on various configurations of PMSG . In sections 3.2 and 3.3, different categories of PM synchronous machines are described. In section 3.4, implementable
winding techniques with their effect on performance are given. Final section focuses
on thermal analysis of PM machines.
3.1.1
DC Generators
The application of DC generator in wind energy systems is not widely spread,
mostly because of the high maintenance requirement of brushes and commutator
and a need of a full scale inverter in order to get connected to the Alternative
Current (AC) grid.
Usually, DC generators are restricted to non-grid-connected wind energy systems
with small DC loads, i.e. battery chargers [2].
3.1.2
Induction Generators
Induction generator consumes reactive power which leads to a poor power factor
of the machine. The power factor of smaller induction machines is lower compared to
larger ones. The consumption of reactive power is penalised by many grid operators,
since it causes losses in the grid. Some solutions are offered for active or passive
compensation of reactive power. They include capacitor banks 1 or condensers 2 .
1
2
passive solutions
active solution
19
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Hence these solutions are costly.
Fixed Speed
Fixed speed wind energy systems including conventional Squirrel Cage / Short
Circuit Induction Generator (SCIG) and a gearbox have been in use for decades. A
big advantage is simplicity in operation and control of the system, however, there
are also some disadvantages. In general, the wind is gusty and turbulent particularly
in urban areas, which very often varies the speed of the rotor and as a result a lower
average efficiency is gained. Normally, dynamic disturbances are unavoidable in
operation of the wind systems. They can occur in the turbine, e.g. variation in the
shaft power, and in the grid, e.g. short circuits. However, in fixed speed systems
the damping is low. Disturbances from the turbine and the grid influence each
other harshly. Inrush current is, furthermore, an issue in wind systems with large
induction machines. Figure 3.1 shows a block diagram of a typical fixed speed wind
system including conventional SCIG gearbox and a transformer. A fixed speed IG
solution including gearbox is suggested in chapter 4
Multi speed IG is suggested for improving the average efficiency in areas with
gusty and turbulent winds. An electrical machine with usually two speed steps is
chosen. First step works in partial load conditions with low wind speeds while the
second works in full load conditions with high wind speeds. There are different
waysof such a system implementation. One solution, which also is the simplest one,
is to have one IG with two different windings and two different numbers of poles.
The second and more common solution is to utilise two induction machines. In
both implementations, it will be possible to improve the average efficiency as well
as the average power factor. The latter solution has been used in Danish wind
systems during 80s and 90s [13]. Still, a complicated control system for switching
between the steps remains an issue. Furthermore, cost of two windings in the former
solution and cost of two IG s in the latter makes the multi speed wind systems more
expensive.
Double Fed Induction Generator
Double Fed Induction Generator (DFIG) is a variable speed wind system including induction machine where also the rotor is connected to the grid. Part of
the power is either provided from the grid or delivered to the grid through the rotor. This power is called the slip power. Frequency of the slip power is varied in
such a way that the rotor field frequency is maintained constant. Variation of the
frequency of the slip power is established by means of two power electronics back
to back converters. Bidirectional flow of the power in the back to back converters
gives the opportunity to work in subsynchronous mode as well as oversynchronous
mode. Back to back converter in DFIG consists of one machine-side-converter, a
DC link capacitor and a grid-side-converter. Role of the machine-side-converter is
to control the speed or the torque of DFIG and the machine power factor, while
20
3.1. DIFFERENT TOPOLOGIES OF ELECTRICAL MACHINES
Figure 3.1. Block diagram of a fixed speed wind energy system including a conventional SCIG, a gearbox and a transformer [2].
the role of the grid-side-converter is to minimise DC link capacitor’s voltage ripple.
Figure 3.2 shows block diagram of a typical DFIG including a transformer.
The benefit with this solution is the possibility of utilisation of conventional
induction generators in a wider speed range and still obtain high efficiency. Because
the converter is connected to the rotor, it only has to carry part of the power instead
of entire rated power. Thus, the converter in DFIG is dimensioned in accordance to
the required speed range. Usually the operating speed range does not exceed ±40
% of the synchronous speed. In most of the wind systems on the market today, this
is ±30 %. In [14], it has been shown that the converter rated at 30 % of generator
rated power is adequate for control of wind turbine rotor within a reasonable speed
range. In other applications which will be introduced later on, the converter is
dimensioned for the full power. Thus the cost and the losses of the converters in
DFIG are lower in comparison to full power converters. This might be an issue for
large wind systems. Other advantage is that the reactive power can be controlled
independently from the active power. It means that DFIG can operate close to the
unity power factor. The drawbacks with conventional DFIG s with gearbox are [2]:
• High maintenance due to the slip rings.
• Limited capability of supplying reactive power.
• High torques in the machine during faulty conditions.
• Additional measures are required to limit the start-up current.
Moreover, the most complex control, especially regarding converters in wind systems
are related to DFIG , which makes them essentially more economical for large wind
systems rather than small systems.
21
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.2. Block diagram of a typical DFIG including a transformer [2].
3.1.3
Synchronous Generators
The synchronous machines have many advantages over induction machines. One
of them is a higher efficiency. It is because the magnetising current is not a part
of the stator current. In induction machines reactive power for rotor excitation is
carried by stator winding as well as the active power for conversion. Accordingly,
synchronous generators will have better efficiency and better power factor. In variable speed wind systems, usually, the synchronous generators are connected to the
grid via a power electronic converter. The amount of deliverable active power from
Synchronous Generator (SG) depends on rating of a converter in Volt-Amperes and
the power factor of SG . Thus, for the same rating of the converter, the closer the
power factor gets to unity, the more active power can be delivered.
Additionally the rotor speed does not depend on the electrical load conditions.
In wind systems it is more convenient to control the rotor speed merely based on the
wind speed. The other advantage is that they can have longer air gaps compared to
induction machines. In induction machines, the airgap length is kept small to limit
the magnetisation current and to improve the power factor [15] . In synchronous
machines, on the other hand, it is desirable to have a longer airgap as it helps to
reduce armature reaction and the synchronous reactance which in turn improves
the stability.
Fixed speed wind systems with SG have the same disadvantages as their IG
counterparts. The dynamics of the grid and the wind turbine are transferred to
each other without considerable damping which can lead to the loss of synchronism
with the grid. Since the rotation speed is determined by the frequency of the grid,
the system becomes even more sensitive. In addition, there is also need for starting
and synchronising equipment too.
The significance of a variable speed wind systems equipped with a SG lies in their
capability to meet the aerodynamic requirements in the widest speed range. To keep
the tip speed ratio at its optimum, the wind turbine rotor speed varies proportional
to the wind speed. This, unlike IGs, provides rotor speed independency from load
22
3.1. DIFFERENT TOPOLOGIES OF ELECTRICAL MACHINES
conditions. Wide operational speed range, from zero to rated speed, is beneficial
for control purposes.
Operational advantages of a SG with power electronics converters are numerous,
like for example voltage regulation which is handled by the grid-side-converter.
Another advantage is that dynamic disturbances of the grid and the wind turbine are
isolated from each other and SG is not at risk of losing synchronism. Furthermore,
starting and synchronising equipment is not needed as this is taken care of by power
electronics converter. The only advantage of IGs over SGs is that the converter is
not dimensioned for full power. However, with recent decrease in cost of power
electronic components, this is not of concern anymore.
Wounded Rotor Synchronous Generator
Wounded Rotor Synchronous Generator (WRSG) s have been scope of research
for many years. The main advantage of WRSG over PMSG is that it intrinsically can
produce reactive power and subsequently regulate the voltage. Thus it is possible to
control the power factor according to electrical load conditions. In power production
WRSG injects the reactive power to compensate loads’ reactive power consumption.
Nonetheless the WRSG has not gained popularity among the wind turbine manufacturers. It is mainly because that the brushes for DC excitation in WRSG require
maintenance. Mechanical vulnerability of rotor windings arising from rotation leads
to winding insulation damage.
Permanent Magnet Synchronous Generator
Self excitation brings about various benefits. One is the elimination of the rotor
copper losses. Hence PMSG s are more efficient compared to WRSG s. Unlike
WRSG no external power supply is needed. The maintenance is eliminated since
brushes and slip rings as well as the rotor windings are removed.
The common issue with WRSG is the relation between the frequency induced
and the mechanical speed of the rotor. When the wind speed changes, the rotor speed and thereby the frequency of the induced voltage changes. However, in
variable speed applications with PMSG this is usually not of concern since the generator is connected to the grid through a converter that will adapt the frequency of
the induced voltage to the grid frequency. One other consideration is that, unlike
WRSG, the field provided by magnets is not controllable. Thus, it is not possible
to regulate the voltage and the reactive power. In variable speed wind systems, this
is, usually, not an issue since the grid-side-converter regulates the output voltage
and the power factor is determined by the grid. Lower maintenance requirements
and thus lower cost are the main reasons why PMSGs are proposed with variable
speed wind systems.
Yet another issue that needs to be considered is the risk of demagnetisation of
magnets due to the temperature rise; the magnets can be partially or fully demagnetized. In partial demagnetisation the magnetic properties are weakened. In full
23
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
demagnetisation magnetic properties are completely lost and they require remagnetisation which is a tedious task and in some cases impossible and a new rotor is
required. Thus a thermal study is suggested to guarantee that the magnet working
temperature is, in any conditions, preserved low. Additionally, the partial demagnetisation is usually a case during a short circuit where some parts of the magnets
are exposed to high opposing magnetic fields.
In [16] it is shown that PMSG s are more suitable for gearless applications
compared to WRSG s. In comparison of PMSG and WRSG and varying the number
of poles, it can be shown that once the number of poles reaches high values, the rotor
yoke height of WRSG becomes thicker. Consequently, weight and size of WRSG
surpasses that of PMSG.
3.2
PM Synchronous Machines
A direct drive wind energy systems cannot employ a conventional high speed
(and low torque) electrical machines. Hartkopf et al. in [17] has shown that the
weight and size of electrical machines increases when the torque rating increases for
the same active power. Therefore, it is essential task of the machine designer to
consider an electrical machine with high torque density, in order to to minimise the
weight and the size. In [18] and [19], it has been shown that PM synchronous machines have higher torque density compared with induction and switched reluctance
machines. Thus a PMSG is chosen for further studies in this work. However, since
the cost effectiveness of PMSG is an important issue, low manufacturing cost has
to be considered as a design criterion in further steps. There are a number of different PMSG topologies; some of them are very attractive from the technical point
of view. However, some of the state of the art topologies suffer from complication
in manufacturing process which results in high production costs.
PM excitation offers many different solutions. The shape, the size, the position,
and the orientation of the magnetisation direction can be arranged in many different
ways. Here, presented topologies include those of which are investigated for low
speed applications or variable speed applications. This list encompasses radial or
axial flux machines, longitudinal or transversal flux machines, inner rotor or outer
rotor machines and interior magnet or exterior magnet machines. Slotless machines
are not presented here.
3.2.1
Radial Flux or Axial Flux
Airgap orientation can be identified in two different ways. Here a hypothetical
normal vector to the airgap is adopted along the flux direction. The axis of the
machines is assumed to be along the length of the machine in the cylindrical coordinate system. Relation of the normal vector with the axis of the machine decides
the radial or axial topology. If the normal vector is perpendicular to axis, machine
is called radial. If the normal vector is parallel with the axis, the machine is called
axial.
24
3.2. PM SYNCHRONOUS MACHINES
Figure 3.3. Cross sectional view in radial direction and in axial direction, respectively, of a typical radial flux PMSG [21].
Radial Flux Machines
Radial flux machines are conventional type of PMSG s. The manufacturing
technology is well established which makes the production cost lower compared
with the axial one [20]. Furthermore, they are very flexible for scaling, as the
higher power ratings of the machine are achieved by increasing the length of the
machine. In other words completely new design and completely new geometry can
be avoided. They are extensively used in ship propulsion, robotics, traction and
wind systems. Figure 3.3 shows cross sectional view in radial direction and in axial
direction, respectively, of a typical radial flux PMSG .
Axial Flux Machines
Various axial flux topologies have been proposed in recent years and their pros
and cons are categorised. Generally, in axial flux machines length of the machine
is much smaller compared with radial flux machines. Their main advantage is high
torque density, so they are recommended for applications with size constraints especially in axial direction. They have found application in gearless elevator systems,
and they are rarely used in traction, servo application, micro generation and propulsion systems [22]. Figure 3.4 shows cross sectional view in radial direction and in
axial direction, respectively, of a typical axial flux PMSG .
One of the disadvantages with the axial flux machines is that they are not
balanced in single rotor single stator edition. Usually, for a better performance the
rotor is sandwiched between two stators or vice versa. Unlike radial flux machines,
25
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.4. Cross sectional view in radial direction and in axial direction, respectively, of a typical axial flux PMSG [21].
the stator windings are located in the radial direction. A circumferentially laminated
stator is required for reduction of iron losses, which complicates manufacturing
process [23].
Scaling of axial flux machine is another drawback. Unlike radial flux machines,
any increase in length is accompanied by increase in airgap diameter. Hence, to
increase the power rating a new design and a new geometry is needed [24]. One
other way to increase the power rating is by increasing number of stators and rotors.
This, however, makes the machine costly.
3.2.2
Longitudinal or Transversal
In transversal flux machines, the plane of flux path is perpendicular to the
direction of rotor motion. The use of transversal flux machines can be proposed in
applications with high torque density requirement [22]. One attractive property of
the transversal flux machines is that the current loading and the magnetic loading
can be adjusted independently. They are proposed for wind systems, free piston
generators for hybrid vehicles and ship propulsion [22]. Figure 3.5 shows a fraction
of a typical transversal flux PMSG. Both PMSGs in Figures 3.3 and 3.4 are of
longitudinal type.
One drawback of transverse PMSG is high leakage flux which results in poor
power factor. To achieve lower flux leakage, number of poles has to be decreased
which in turn reduces torque density. The task of the designer is to find a compromise between the flux leakage and the torque density of the machine. Further26
3.2. PM SYNCHRONOUS MACHINES
Figure 3.5. Fraction of a typical transversal flux PMSG [22].
more the major drawback with rotational ones is relatively difficult manufacturing
process. Yet another drawback is that, in rotating transverse PMSG, mechanical
construction is weak due to large number of parts.
3.2.3
Inner Rotor or Outer Rotor
The rotor surrounds the stator in outer rotor machines. In these machines, the
magnets are usually located on the inner circumference of the rotor. Accordingly,
for the same outer diameter of the machine, in the outer rotor machine the rotor has
higher radius compared with the stator and it can be equipped with higher number
of poles for the same pole pitch [21]. Another advantage is that the magnets are well
supported despite the centrifugal force. Furthermore a better cooling of magnets
is provided. Outer rotor machines are common for small HAWT turbines, where
sometimes the hub carrying the blades is directly fixed to the rotor [25].
However, the inner rotor machines are a more common solution present on the
market today. In small machines, the main contributions to the losses are copper
losses and therefore the stator winding has the highest temperature rise in the active
material of the machine.
Hence, it is more beneficial to put the stator winding, rather than the magnets,
closer to the housing, where the cooling properties are good. This causes less temperature rise for the same amount of losses. Figure 3.6 shows an inner rotor PMSG
and an outer rotor PMSG .
27
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.6. Inner rotor PMSG (left) and an outer rotor PMSG (right) [26].
Figure 3.7. A surface mounted rotor for a PMSG [15].
3.3
PM Configurations
The PMSG can be divided into different topologies depending on the magnet
arrangement on the rotor. These are introduced below. However, it should be
mentioned that the rotor configurations are not restricted to the given examples,
e.g. in interior magnets various configurations are implementable.
3.3.1
Surface Mounted Magnets
A common topology is where the magnets are mounted on the surface of the rotor, sometimes referred to as exterior magnet, but, more known as Surface Mounted
Permanent Magnet (SMPM) machine. The magnets are glued and/or bandaged to
the rotor surface in order to withstand the centrifugal force. Usually, the magnets
are oriented or magnetised in radial direction and more seldom in circumferential
direction. The direct and quadrature reactances are almost equal. Construction of
the rotor core in SMPM is the easiest among different PM configurations due to
simple rotor geometry. Figure 3.7 shows a surface mounted rotor for a PMSG.
28
3.3. PM CONFIGURATIONS
Figure 3.8. Two different inset magnet rotors for PMSGs [15].
3.3.2
Inset Magnets
In inset magnet machines, rotor core of SMPM machine is modified with iron
interpoles. Iron interpoles are protrusions of rotor core wherever magnets are not
present on the surface. Interpoles cause saliency and the inductances in direct
and quadrature directions are different. In these machines, part of the torque is
reluctance torque and the torque density is higher compared to SMPM . The
magnets are radially magnetised. The flux leakage is higher in comparison to SMPM
which results in lower power factor.
Therefore, in direct drive application, the inverter utilisation is lower compared
to geared applications. This topology is not common in gearless wind systems.
Figure 3.8 shows two different inset magnet rotors for PMSGs.
3.3.3
Buried Magnets
In this configuration the magnets are put inside the rotor and therefore it is
referred to as Interior Permanent Magnet (IPM) machine. There are many different
ways in achieving interior magnet configuration. The magnets can be magnetised
in radial direction as well as circumferential direction. The thickness of iron bridges
between the magnets has to be designed carefully to avoid saturation. Again, the
inductance in quadrature axes is different from that in direct axes direction. Figure
3.9 shows six different buried magnet rotors for PMSGs.
The main advantage of this PM configuration is that weak PM material such as
ferrite can be used. Another advantage is magnetic protection against short circuit
conditions [15]. It is because in faulty conditions, iron bridges between magnets
get saturated which prevents high reverse demagnetising field to reach the magnets.
This topology is suggested for high speed applications due to mechanical strength
of the rotor against the centrifugal force.
Burying magnets in production stage is a complicated process. Moreover a nonferromagnetic shaft is vital, otherwise a large part of magnets’ flux penetrates the
shaft, which is located nearby, and it will not be utilised for magnetisation of the
29
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.9. Six different buried magnet rotors for PMSGs [15].
airgap. Like inset magnet machines, the flux leakage is high which reduces the
power factor, the efficiency and the inverter utilisation.
In [21] , F. Libert studies two different buried magnet topologies and concludes
that both gives rise to manufacturing problems. One is called V-shaped buried
magnet design and the other is called tangentially magnetised buried magnet design.
The author also mentions some saturation problems when the number of poles is
high. This is a common problem for the buried magnet topologies. If the number of
poles increases, the distance between magnets decreases (when rotor core diameter
is kept constant). Therefore, the narrow iron bridges get saturated more easily.
Figure 3.10 shows cross section of a pole pair of a V shaped buried magnet design
(left) and a tangentially buried magnet design (right).
3.4
Winding
The windings can be divided into overlapping and non-overlapping categories.
Over lapping windings can be wound either distributed or concentrated. Non overlapping windings can be wound solely in concentrated way. Figure 3.11.a) shows
a distributed overlapping winding with Qs = 24 and q = 2 for a four pole machine.
Figure 3.11.b) shows a concentrated overlapping winding with Qs = 12 and q = 1.
Figure 3.11.c) shows a double layer concentrated non-overlapping winding with
Qs = 6 and q = 0.5, which is the traditional concentrated winding. Figure 3.11.d)
30
3.4. WINDING
Figure 3.10. Cross section of a pole pair of a V shaped buried magnet design (left)
and a tangentially buried magnet design (right) [21].
shows a single layer concentrated non-overlapping winding with the same values of
Qs and q as Figure 3.11.c).
The term overlapping is usually omitted. For instance "overlapping distributed
winding" is almost always referred to as distributed winding. In this text, on
the other hand, "concentrated winding" stands for "double layer concentrated nonoverlapping winding".
3.4.1
Distributed Winding
Distributed winding has been used for Brushless Alternative Current (BLAC)
machines for decades. One of the advantages of distributed winding is that it can
give high value of winding factor when q is high and the full pole pitch is chosen.
Nonetheless, it has some drawbacks, like for instance its long end windings. End
windings do not contribute to induction of the phase voltage. The role of end
windings is limited to carry the current from one coil to the other. Thus, end
windings are associated with copper losses and it is desired that the end windings
are as short as possible. In distributed winding, when the coil sides are far from
each other, the copper losses will be higher and the axial length of the machine will
be longer. Thus distributed winding reduces the efficiency of the machine. If the
size of the machine is a critical design parameter, the concentrated winding should
be considered.
3.4.2
Concentrated Winding
In concentrated winding the coil turns are concentrated around one tooth and
therefore it will benefit from short end windings due to non-overlapping property.
Another advantage is better heat conductivity between the winding and the tooth.
Furthermore, segmentation of stator core teeth is possible [28]. In this way, the
windings can be pre-pressed and the coils can be made with rectangular shape,
which, in turn, will give high slot fill factor and high torque density.
Concentrated winding exhibits high fault tolerance on SMPM s and is associated
with increase in leakage inductance [29]. Implementation of concentrated winding
31
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.11. Windings in low speed PMSG a) distributed overlapping winding.
b) concentrated overlapping winding. c) double layer concentrated non-overlapping
winding. d) single layer concentrated non-overlapping winding [27].
increases leakage inductance which in turn limits high currents in short circuit
conditions. In fact in faulty conditions, the excitation field of WRSG is reduced
to protect the machine. However, excitation of PMSG is not controllable. Hence,
introduction of higher flux leakage may be an advantage. In addition, due to nonoverlapping property, coils are physically and thermally seperated in a better way
compared with distributed windings. This reduces the risk of phase to phase short
circuit in the event of damaged winding insulation. Furthermore, the torque ripple in
SMPMs with high pole numbers and concentrated windings is reduced [21]. Higher
flux weakening capability is another characteristics of concentrated winding.
32
3.4. WINDING
Fractional Slot Winding
One disadvantage with traditional concentrated winding, where q = 0.5 , is a
lower winding factor compared with distributed winding. The reason is that the slot
pitch is 2/3 of the pole pitch and, neglecting the flux leakage due to iron saturation,
only 2/3 of the magnet flux is linked to the stator. As a consequence, winding factor
drops to 0.866 and torque rating of traditional concentrated winding is reduced by
the same factor.
To cope with this drawback, fractional slot concentrated winding are suggested,
which utilises any feasible combination of p and Qs . Thus, it is possible to have
higher winding factors with higher torque density. In applications where weight and
size are critical design parameters, the fractional winding may be of interest.
F. Magnussen in [20] and F. Libert in [21] have studied numerous slot pole
number combinations of fractional slot winding and have categorised them regarding
their parasitic effects. It has been reported that selection of pole and slot numbers
has to be chosen very carefully because of the parasitic effects that arises with certain
combinations. These parasitic effects include, cogging torque, radial magnetic forces
and alternating magnetic fields with high frequency. The disadvantage with radial
forces is vulnerability to magnetic noise, while high frequency magnetic flux leads to
eddy current losses in the rotor and the magnets. Some counter active measures have
been suggested by F. Magnussen like: magnet segmentation, rotor core lamination
and high mechanical rigidity of core [20] 3 .
In [21] F. Libert has studied fractional slot winding in terms of winding factor,
harmonic content of Magneto-Motive Force (MMF) , torque ripple, cogging torque
and magnetic forces. The study have been carried out on the design with pole
numbers between 4 and 80 and slot numbers between 6 and 90. Slot pole number
combinations are divided in few categories and general conclusions are drawn for
each category. The categories where Least Common Multiple (LCM) is high, enjoys
from the biggest reduction in cogging torque. The highest LCM is achieved where
slot pole numbers have values very close to each other, i.e. p = Qs ±1 . However, the
machines with these combinations are asymmetrical. This gives rise to radial forces
and magnetic noise. The author, ultimately, suggests that the slot-pole number
combinations with high winding factors and with symmetrical winding layouts have
to be chosen.
IPM s with concentrated winding have lower torque density than that with
distributed winding. Concentrated winding decreases saliency ratio in IPM and
accordingly the reluctance torque reduces as well. This means that an IPM with
concentrated winding will have lower peak torque and also lower torque density.
Reduction of torque density can be compensated with additional iron laminations
in axial direction as the length of the machine become shorter due to concentrated
windings; This, however, is costly [30] .
3
see section 3.5.4
33
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
3.4.3
Single Layer Concentrated Non-Overlapping Winding
An advantage of a single layer concentrated windings is simpler automatised
winding process and better fault tolerance compared to their double layer counterparts. They use every other tooth for winding which results in the simpler automatized winding. The better fault tolerance comes with better physical and electrical
separation between coil turns.
Although the benefits with this winding looks attractive, the double layer windings are actually more common today. It is mostly because single layer winding
suffers from longer end windings and higher inductance.
3.5
Thermal Behaviour
There are different sources of losses in electrical machines i.e. iron losses, copper
losses, etc. The losses give rise to temperature, which has dramatic influence on
performance and lifetime of electrical machines. Hence, study of thermal behaviour
of an electrical machine is vital.
The temperature rise in the machine is strongly dependent on the load. In wind
systems, the speed and the torque are very often lower compared with the ratings
of the machine and varies with the wind conditions. The advantage is that the
average temperature rise will be lower in comparison to the rated operating point.
However, in order to guarantee high performance and long lifetime in any operation
condition, the thermal calculations are performed based on the rated operation.
In the following subsections, consequences of temperature rise are presented and
different cooling systems are discussed. A brief introduction to heat transfer theory
is given, while more detailed theory is left for the reader. The most emphasis is put
on introduction of sources of losses in the last subsection.
3.5.1
Consequences of Temperature Rise
Performance
Thermal loading determines pretty much the power rating of the electrical machine. Values such as current density are often limited to a certain value depending
on the cooling conditions in an electrical machine. This bounds current loading
and respectively torque rating of the electrical machine. In other words, even if
it is possible to manufacture more compact machines with higher torque densities,
cooling capability restricts further reduction in the size.
Lifetime
The lifetime of an electrical machine is also affected by the so called thermal
ageing, which influences the insulation. One of the requirements on winding insulation is to transfer the heat and to tolerate thermal stresses during normal and
34
3.5. THERMAL BEHAVIOUR
Insulation Class
A
E
B
F
H
Hot Spot Temperature in ◦ C
105
120
130
155
180
Table 3.1. Different classes of an insulation material due to IEC − 85.
faulty conditions. Commercially available insulation material can tolerate limited
temperature rise. Table 3.1 summarizes standardised temperature rise categories.
Acceptable lifetime is expected, if the insulation material working temperature
conforms to above conditions. On the other hand, due to an empirical law, lifetime
of an insulation material halves with every 10 K extra temperature rise above the
nominal temperature.
Temperature influences magnet characteristics and it can increase risk of demagnetisation. Figure 3.12 shows B-H curve of a typical PM material for different
temperatures. The coercivity and remanence flux density decrease when the temperature increases. The knee point also moves upwards. The working point shifts
on working line of the magnetic circuit downwards when the temperature increases.
Given a high enough temperature and an improperly designed magnetic circuit, the
working point will drop below the knee point, where the magnet loses its magnetic
properties. If the machine is to be run again, PM has to be remagnetised, which is
a complicated and tedious task.
Overload increases the risk of demagnetisation. In these conditions the temperature exceeds the rated value and the remanence flux density of magnet decreases. If
the magnetic circuit is not properly designed, PM magnetic flux will reduce remarkably. In order to compensate the reduction of the magnetic flux, the control unit
will tend to increase the current in the stator winding, since the load torque should
be kept the same. As a result, copper losses in the windings are increased and the
temperature raises more in the windings and eventually in the magnets. This leads
to even higher reduction of remanence flux density. In theory, reoccurrence of this
cycle can eventually lead to demagnetisation of the magnets. However, in order
to avoid demagnetisation during overload conditions, protection equipment against
over-temperature condition is offered.
Among PMSGs, Inset magnet machines and SMPMs are more vulnerable and
are at a greater risk of demagnetisation compared to their IPM counterpart. Iron
bridges around the magnets in IPMs saturates during faulty conditions and they
counteract penetration of strong reverse field into the magnets. However, the temperature rise can still be high, because the magnets are buried and the cooling of
magnets is more difficult.
35
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Figure 3.12. A typical magnet characteristics curve [20].
3.5.2
Cooling System
Cooling system facilitates dissipation of the heat, which will reduce temperature
rise in the machine. Usually electrical machines are forced cooled by air or water. In
air cooled machines a fan forces the air along the airgap. In water cooled machines
the pump forces the water through tubes that are located in ducts. There are
different possibilities for putting the ducts inside the machine, they can be located
axially or spirally. Moreover, they can be located within the mantel (frame) or in
the stator core. Putting ducts in stator core provides better heat transfer, however,
it influences the manufacturing process of the stator laminations.
Kylander has developed an analytical model for thermal analysis of induction
machines based on experimental results [31]. The model introduces thermal resistances. Lindström has developed a thermal model for a PMSG [32].
3.5.3
Heat Transfer Theory
Heat transfer is a result of a difference in the temperature. The heat is always
transferred from higher temperature towards the lower temperature. It occurs in
three different forms namely conduction, convection and radiation.
36
3.5. THERMAL BEHAVIOUR
Conduction
Heat transfer through a substance is defined as conduction. The substance can
be in any state: gas, liquid or solid. To measure conductive property of a material
thermal conductivity is introduced. Usually the value of the thermal conductivity
of materials lies in the range between 0.026 W/m/K for air and 427 W/m/K for
silver [33]. Conduction is modeled by Fourier’s law which also can be applied when
heat is generated inside the body. However, when the time variation of conduction
is considered, specific heat capacity of the body, which represents thermal capacity,
is also introduced. In steady state analysis, however, this is neglected.
In the field of electrical machines, conduction is the most common form of heat
transfer in both steady state and transient conditions.
Convection
Heat transfer from a heat source by means of fluid movement is defined as
convection. Fluid flow is caused by an external force either in natural or in forced
conditions. In the former, discrepancy in fluid density creates the force; In the
latter the force is caused by a pump or a fan. To measure convective property of
a fluid, heat transfer coefficient is introduced. Average heat transfer coefficient of
a fluid lies in a range between 6 W/m2 /K for natural air convection and 120, 000
W/m2 /K for condensing of steam [33]. Estimation of this value is complicated, since
it depends on many variables like geometry of the surface, temperature difference,
flow mechanical characteristics and physical characteristics of fluid i.e. viscosity.
Convection is explained by Newton’s law of cooling.
In the field of electrical machines, convection is the second most common form
of the heat transfer in the steady state, but it does not play a remarkable role in
transient conditions.
Radiation
Heat transfer by means of radiation does not need any substance. Thermal
radiation is a function of couple of parameters as reflectivity, temperature difference,
emissivity and geometry. It is modeled by Stefan Boltzman’s law. In electrical
machines the amount of radiation is negligible.
3.5.4
Losses in PMSG
The main function of an electrical generator is to convert energy from mechanical
into electrical. However, a part of energy is lost during this process which is referred
to as losses. In electrical machines losses are divided into two categories i.e. normal
losses and stray losses. Stray losses are additional losses that arises in an electrical
machine aside from the normal losses considered in usual performance calculations
for motor efficiency [15]. The main part of the stray losses are usually caused by
eddy currents due to the leakage flux.
37
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
The normal losses involve copper losses in stator windings, iron losses in stator
and mechanical losses such as friction. The iron and the copper losses are the biggest
contributors to the losses in PMSG . One advantage of PMSG over IG is elimination
of the copper losses in the rotor, namely slip loss [34] . Estimation of normal losses
is easy and the corresponding knowledge is well established. On the other hand
estimation of stray losses is complicated as they depend on many parameters. This
complication might lead to inaccuracy in the calculations of the thermal behaviour
of the machine. A thorough discussion of losses is presented in order to improve a
better perspective over variety of origins of losses.
Stator Core Losses
Various phenomena associated with variation of magnetic flux results in the
stator core losses. Among them, the rotational and excess losses are probably less
well known while the hysteresis and eddy current are more familiar. Here, hysteresis
and eddy currents losses are introduced first together with Epstein frame test. Then,
the two former are presented. Finally counteractive measures are suggested.
Eddy currents are induced in the stator iron due to variation of magnetic field
based on the Faraday’s Law and they create losses based on the Ohm’s Law. The
amount of losses depends on the time rate of change of magnetic flux density. Assuming sinusoidal variation of magnetic flux density, eddy currents loss will depend
on electric properties of material as well as applied field, including frequency and
maximum value of magnetic flux density.
Hysteresis losses are caused by magnetic properties of ferromagnetic material
in a time varying magnetic field. The amount of these losses depends mostly on
the magnetic properties of the material but also on the applied field, including its
frequency and maximum value of magnetic flux density.
To estimate the iron losses in the stator, the results from Epstein frame test
are used in analytical calculation. Accurate prediction of iron losses is much more
difficult in comparison to copper losses. Accordingly, steel manufacturers provide
the machine designer with results from the Epstein frame test. In this test the iron
losses of steel material, subjected to various magnetic flux densities (in terms of
amplitude and frequency) are measured. Simplified analytical models are developed
to estimate the iron losses in electrical machines based on the results of Epstein
frame test. These analytical methods are validated by means of comparison to
experiments on similar machines or FEM simulations.
Angular direction of magnetic field is, usually, constant in the stator. But it
varies in regions of stator where the teeth and the yoke are connected to each
other. This results in rotational loss. In the region where it exists, it adds to the
core losses. Excess loss is not a well-known phenomenon. In order to include the
effect of rotational and excess losses, the value of estimated core losses is, usually,
multiplied by a correction factor.
Calculated results of core losses may differ from the experimental results for
a number of reasons. Applied field in the machine is assumed to be uniformly
38
3.5. THERMAL BEHAVIOUR
sinusoidal in different physical points and the magnetic properties of the material
are assumed to be uniform. However, in real machines these conditions are not
prevailing perfectly. A waveform of the magnetic flux density is non sinusoidal and
non uniform. Influence of harmonics, which results in non sinusoidal magnetic flux
density, on the core losses will be introduced later in the text. Furthermore, the
magnetic property of material varies when it is subjected to mechanical stresses
during manufacturing e.g. punching.
There are various solutions available in order to reduce the core losses. Some
more common are laminated core with thin iron lamination, high resistivity and
alloyed contents like silicon. These measures reduce eddy current losses. Another
solution in order to reduce the iron losses is to reduce nominal frequency. However,
the frequency is proportional to the rotor speed and to the number of poles. As
the rotor speed is determined by the application, the frequency, therefore, cannot
be chosen arbitrarily. Furthermore, increasing the number of poles reduces the pole
pitch which in practice cannot be chosen too short.
Laminations are annealed after they are stamped or cut, in order to compensate
the manufacturing stresses. Variation of magnetic characteristics in cut edges is
then avoided.
Mechanical Losses
Mechanical losses are relatively small in comparison to other losses especially in
low speed applications. It encompasses two parts, namely windage and bearing.
Windage losses are caused by mechanical friction of air and rotor surface. It
depends on various parameters and phenomena and it is quite complicated to calculate more accurately. For instance it depends on gas properties and the prevailing
gas flow characteristics. In electrical machines the gas flow is mostly turbulent in
high speed applications and it is laminar in low speed application. An experimental
equation in [35] gives a rough estimate of windage loss.
3 4
Pwindage = Cf ρπωm
R L
(3.1)
where ρ is the mass density of the gas, ωm is the mechanical angular speed of
rotor and R and L are radius and length of the airgap cylinder respectively. Cf is
the friction coefficient which is empirically determined.
Mechanical loss in the bearings depends on parameters like bearing type, lubricator physical characteristics, shaft mechanical load and rotor speed, where lubricator
characteristics are dependent on the temperature. An experimental equation in [35]
gives a rough estimate of bearing loss.
3
Pbearing = Cb Dm
ωm
(3.2)
Dm is the average diameter of bearing and Cb is the bearing coefficient, which
again is an empirical factor.
39
CHAPTER 3. ELECTRICAL MACHINES FOR WIND ENERGY SYSTEMS
Stray Losses
Stray losses are divided into stray no-load losses and stray load losses. Generally,
the former is represented by permeance variation and the latter is represented by
leakage flux. Space harmonics’ origin is due to the non-sinusoidal distribution of
windings, saliency and slotting effect in an electrical machine. Time harmonics
are generated by power electronics converters operated with electrical machines.
High frequency of parasitic effects results in induction of eddy current in metal
parts. Active material of the machine like stator conductors, rotor core and rotor
permanent magnets are prone to stray losses.
In the following, stray losses are introduced based on the location of losses.
First AC winding losses are discussed, second stray losses in permanent magnets
are described and finally stray losses in rotor core are mentioned.
Stator Winding
Eddy currents are induced in the stator windings in the form of skin and proximity effects. If the source of varying applied field is the winding itself, the phenomenon
is called skin effect. If the source of varying applied field is an external origin like
rotor magnets, the phenomenon is called proximity effect. Eddy currents originating from skin and proximity effects in machines will give rise to non uniform current
density distribution within the conductor, i.e. less concentration in the centre and
more concentration on the circumference. As a consequence, effective cross section
area for the current will be lower compared with the available cross section. This
leads to higher AC resistance and higher losses.
Permanent Magnets
Eddy currents losses can be induced in permanent magnets in certain conditions.
As mentioned, certain slot pole number combinations in concentrated winding design will result in space harmonics. This influence is more pronounced in high speed
machines with high frequency. F. Sahin in [35] suggests an analytical estimation
of eddy current losses in permanent magnets. In order to reduce these losses a
proposed solution is magnet segmentation. In general no load stray losses caused
by permeance variation can be reduced by increasing the airgap length or by using
magnetic wedges.
Rotor Iron
Eddy currents losses can be induced in rotor core in certain conditions. In absence of parasitic effects, the magnetic flux density in the rotor iron is constant.
Harmonics, e.g. created by the slotting effect, distort magnetic flux in the rotor.
However, in SMPM machines, effective airgap is large and these losses are insignificant [12]. Again these losses are more pronounced in high frequency machines, but
40
3.5. THERMAL BEHAVIOUR
it should be mentioned that a careful selection of slot pole number combination in
concentrated winding is mandatory.
41
Chapter 4
Induction Generator
A multiple step fixed speed WECS including induction generator is already
proposed in section 3.1.2. In order to work as fixed speed wind system, the system
has to be operated at speeds higher than synchronous speed. Induction machine
is able to start in Direct Online (DOL) mode. DOL means that an induction
machine, which is at standstill, is able to accelerate when it is directly connected
to the grid. Another benefit in fixed speed WECS with induction generator is less
mechanical stress on the drive train compared with synchronous machine. Usually,
the induction generator is operated between the synchronous speed and just above
the synchronous speed. The dynamic disturbances in the grid and from the wind
turbine will be reflected in the variation of the slip i.e. the speed of the machine.
One disadvantage with the induction generator is reactive power consumption.
Therefore, induction generators require some form of reactive power compensation.
This can be provided with introduction of capacitor banks. Some control of the
capacitor banks should be implemented due to the power variation of the load.
However, this may add some extra cost. Another disadvantage with the induction
generator is their so called inrush current. During starting, the current in induction
machine is high, which may cause some damage to the windings.
4.1
Fixed Speed Induction Generator
Fixed speed wind turbine is still a popular concept in the rapidly growing global
wind market. Figure 4.1 shows the market share of installed fixed speed WECS
in large wind turbine market. The cost of power produced by WECS is a function
of capital cost, system reliability and the energy yield. According to the theory,
energy yield of variable speed WECS is higher compared with the fixed speed one.
However a lower capital cost and higher reliability makes the fixed speed WECS
an attractive solution. Values between 4 % - 20 % have been reported for the
increase in energy yield by utilizing variable speed instead of fixed speed systems.
The reason for variation in the reported values is the methodologies adopted by
different researchers. Therefore, in this chapter a more cost effective fixed speed
43
CHAPTER 4. INDUCTION GENERATOR
Figure 4.1. Time variation of market share of yearly installed power of fixed speed
WECS (including induction generator, capacitor banks, soft starter and output transformer) [37].
WECS is to be verified.
One possible topology for fixed speed WECS is an induction generator connected
to the line where the load is located in between. The grid maintains the voltage
and the frequency and provides the machine with magnetizing current which is
associated with reactive power consumption. As a result, the machine is capable
of production of active power. The power produced by the generator may exceed
the power consumption by the load and the remaining power can be injected to the
grid. However, there should be an agreement between the grid operator and the
owner of the generator how to regulate the injected power [36].
4.2
Selection of Induction Motor as Generator
Induction machines are the most prevalent motors on the market. Therefore, in
order to utilise an induction machine as generator a few considerations has to be
taken into account.
44
4.3. TWO STEP FIXED SPEED INDUCTION GENERATOR
4.2.1
Temperature Rise
A higher permissible temperature rise has to be considered due to the special
requirements by the application as well as distinction between performance in motor
and in generator mode. The required lifetime of the machine is 100, 000 hours. The
main constraint on working lifetime of an induction machine is the thermal ageing
of the winding’s insulation material. However, the guaranteed working lifetime of
an insulation material according to the standards, regardless of insulation class,
is 20, 000 hours. Therefore a 25 ◦ C safety margin is suggested to guarantee the
required lifetime.
4.2.2
Efficiency
Efficiency of the induction motor working as generator is lower for the same slip.
Therefore, it is recommended that high efficiency induction motors are chosen for
generator applications. In order to increase the efficiency of the induction machine,
thinner iron lamination together with the lower loss density material can be used
and also copper with high conductivity properties in windings.
4.2.3
Size
It is suggested that the power rating of the induction machine should be around
25 % higher compared with the power rating of the wind turbine. Efficiency of
an induction machine is maximum at the rated slip. For a small scale induction
machine this can be around 80 % . Therefore the size of the induction motor should
be selected in such a way that at full load, the machine works at 80 % of its rating
[38]. This ensures that the temperature rise, while working either as a motor or as a
generator is the same. For instance, if a 12 kW induction generator is to be used, size
of the induction machine is 15 kW . One should consider that in motor operation
mode, the hot spot is in the stator winding, since the power losses in the stator
winding are the major fraction of the losses in the machine. In generator operation
mode, the corresponding power loss has to be provided from the shaft power and
later on delivered to the stator winding via the rotor and the airgap. This causes
some additional copper losses in the rotor and therefore further temperature rise in
the rotor [38]. Hence, for the same temperature rise in the machine, the induction
generator has to be derated.
4.3
Two Step Fixed Speed Induction Generator
Multiple step fixed speed WECS is proposed to increase energy yield of fixed
speed wind system. Rotation speed of the wind turbine in a fixed speed WECS
including an induction generator is determined by the induction machine’s operating
range. Therefore in a single step fixed speed system, selection of a gear ratio is of
concern. Since the rotation speed will be maintained independent of the wind speed,
45
CHAPTER 4. INDUCTION GENERATOR
the tip speed ratio will vary quite often. This means that the power coefficient
deviates from its optimum value. The choice of the wind speed corresponding to
the optimum tip speed ratio influences selection of gear ratio and vice versa. If a
low gear ratio is selected, the rated wind speed is at a high wind speed and for low
wind speeds the power coefficient is low. On the contrary, if a high value for gear
ratio is chosen, the machine rotates slowly and the rated wind speed is at a low
wind speed and then power coefficient drops for high wind speeds [39] .
The concept of two step induction machine aims to have high value of power
coefficient for both low and high wind speeds. With a two step induction generator,
it is possible to adapt the rotation speed of the system to the prevailing wind speed
for the same gear ratio. Therefore, the variation of the tip speed ratio is halved.
Two step induction generators with two different windings have two different pole
numbers. The low speed step works at low wind speeds while the high speed step
is at high wind speeds.
The list of functions that have to be provided in a multiple step WECS is:
• Measurement of wind speed and direction.
• Starting command to the machine (to start as a motor).
• Switching command (between the two steps) to the generator.
• Mechanical brake for the wind turbine.
• Overload protection.
• Command of switching in the electrical load.
However a multiple step IG working in a WECS suffers from [40]:
• Switching transients when changing poles.
• High torque peaks with machines designed for low rated slip and high losses
with machines designed for high rated slip.
• Lower energy yield in comparison to variable speed WECS.
4.4
Self Excited Induction Generator
It is suggested that a two step fixed speed WECS is equipped with a capacitor
bank. A simulation study has been done by S.S. Murthy et al considering inrush
current, reactive power and efficiency of a single step 55 kW induction generator
together with a fixed speed wind system [39] . The results shows that during start
of the electrical machine, the motor inrush current reaches to 6 p.u. and it lasts
for almost 1 second. For the steady state analysis reactive power and efficiency are
studied for different wind speeds. A consistent reactive power, around 0.7 p.u. , is
required from the grid even though the wind speed is very low. Subsequently, the
46
4.4. SELF EXCITED INDUCTION GENERATOR
Figure 4.2. The operating zones of induction machine [41].
produced active power is very low, around 0.03 p.u. . The power factor, therefore,
is very low and varies between 0.043 and 0.67. The efficiency is very poor and varies
between 20% and 40% .
For the case study above, it is obvious that the power factor is too low at low
load conditions. Thus, the power factor correction in some way is required. A
brief discussion on this solution, which sometimes is entitled self excited induction
generator, is presented below. However, in order to minimise the cost of the system,
the final solution with a two step induction generator proposed in this report does
not include a capacitor bank.
Requirements on self excited induction generator for application as wind generator are:
• High efficiency.
• Low voltage regulation.
• Low harmonic contents.
Figure 4.2 shows the operating zones of the induction machine optimised for working either as a generator or as a motor. Induction generator works in both saturated
and unsaturated operating zone. On the other hand the motor works only in unsaturation mode. The diagram is drawn with magnetizing reactance on the horizontal
axis and the ratio of back Electro-Motive Force (EMF) and frequency on vertical
axis.
47
Chapter 5
Analytical Design of PMSG
This chapter treats analytical design of a longitudinal, inner rotor, radial flux,
surface mounted PMSG with concentrated winding. Selection of the machine topology is supported by the discussion in chapter 3. Initially, design requirements and
constraints are presented in section 5.1. The selection of design parameters is described in section 5.2 and then the design procedure is followed. In the last section,
the design objectives are discussed .
5.1
Design Requirements and Constraints
Table 5.1 shows the requirements which has to be fulfilled by the generator.
5.1.1
Mechanical Calculation: Minimum Shaft Diameter
The shaft must be able to withstand the high torque in the machine. The
mechanical calculations for minimum shaft diameter guarantees the safe transfer of
the mechanical power from the machine to the turbine. Rated torque of the machine
Rated power
Rated speed
Base speed
Airgap length
Cooling system
Cogging torque
Outer diameter
Lifetime
Efficiency
Minimum shaft diameter
Pn
nr
nn
δ
Dy
η
Di,min
12 kW
100 rpm
90 rpm
1.5 mm
Natural air convection
around 1%
<2m
100, 000 hours
around 94 %
> 0.1269 m
Table 5.1. Design requirements and constraints.
49
CHAPTER 5. ANALYTICAL DESIGN OF PMSG
Correction factor for strength weakening
of the shaft due to the key slot
Geometrical correction factor
Load dependant correction factor
Safety factor under normal conditions
Yield strength of shaft material
Permissible strength of shaft material
Safety factor under failure conditions
Table 5.2.
diameter.
kkey
4
αmech
βmech
knormal
σyield
σperm
kf ailure
1
1
2
2.2 × 108 N/m/m
4.4 × 107 N/m/m
12
Mechanical parameters involved in determination of minimum shaft
is
Tn =
Pn
2πnn
60
=
12kw
2π×90rpm
60
= 1273N m
(5.1)
1
The bending moment acting on the shaft is chosen to be 10
of the rated torque.
1273 N m
Therefore Mbend =
=
127.3
N
m
Ṫhere
are
two
different
values for mini10
mum shaft diameter which should both be met; one for normal conditions and the
other for failure conditions. The minimum shaft diameter in normal conditions is
√
Di,min,normal =
3
32
σ
π αperm
mech
√
2
Mbend
+ 0.75(βmech knormal Tn )2
(5.2)
And the minimum shaft diameter in failure conditions is
Di,min,f ailure
v
u
u 16kf ailure kkey Tn
3
=t
σyield
π αmech
(5.3)
Table 5.2 shows the parameters used in equations 5.2 and 5.3 1 . Consequently,
Di,min,normal = 0.1269 m and Di,min,f ailure = 0.1123 m
5.2
Design Parameters
Selection of the design parameters is essential for this work. In the following
subsections, they are categorised and justifications are presented. The main criteria
for selections are the cost and the electromagnetic performance.
5.2.1
Material
Active material of the machine includes permanent magnet, steel sheet for the
rotor and stator laminations and copper for windings. Suitable materials are chosen
to provide sufficient electromagnetic performance and average cost.
1
For a better introduction of these parameters, see section 7.1.1 in [15]
50
5.2. DESIGN PARAMETERS
Remanence flux density at 20◦ C
Temperature coefficient of remanence flux density
Mass density
Br0
aP M
ρP M
1.2 T
−0.0009 1/K
7700 kg/m3
Table 5.3. Characteristics of VACODYM 655 AP.
Permanent Magnet
VACODYM 655 AP by Vacuumschmelze GmbH is chosen as the permanent
magnet material. The characteristics of this material are given in Table 5.3. The
vendor produces VACODYM 2 series as well as VACOMAX 3 series. The coice
of VACODYM is because of its high energy density. VACODYM is produced in
different shapes and they are classified in three main categories:
• HR (High Remanence)
• TP (Transverse Pressed)
• AP (Axial Pressed)
VACODYM AP series was chosen since it can have arc segment shape. Figure 5.1
shows magnetic characteristics of VACODYM 655 AP.
Iron
M400 50A by Surahammar Bruk AB is chosen as steel material for stator and
rotor laminations. Selection of this material is fulfilled as a trade off between cost
and electromagnetic performance. Table 5.4 shows the characteristics of M400
50A. Detailed datasheet is given in appendix A . Figure 5.2 shows the magnetic
characteristics of M400 50A.
5.2.2
Geometry
Table 5.5 shows the design parameters corresponding to the geometry. These
are called independent geometry parameters, since their values are independently
chosen from other geometry parameters. Figure 5.3 shows typical geometry of the
machine. Some of the independent geometry parameters can be seen in Figure 5.3.
The geometry variables determined by optimisation are the six first independent
geometry parameters. The rest of the independent geometry parameters are selected
by the designer and selection criterion of the important ones is described in the
present chapter.
2
3
NdFeB base
cobalt base
51
CHAPTER 5. ANALYTICAL DESIGN OF PMSG
Figure 5.1. Magnetic characteristics of VACODYM 655 AP.
thickness
Mass density
−
ρF E
0.5 mm
7700 kg/m3
Table 5.4. Characteristics of M400 50A.
5.2.3
Temperature
Insulation class E is selected for the insulation material. Table 5.6 shows the
nominal temperatures.
5.2.4
Winding (Concentrated)
Based on the discussions presented in section 3.4.2 fractional slot double layer
concentrated winding is chosen. Table 5.7 shows the winding parameters.
Selected pole slot combination is done in accordance to discussion presented in
section 3.4.2, for instance:
• Winding factor is as high as 0.945 .
• The machine is symmetrical with 8 similar sectors.
• Least Common Multiple is as high as 576.
52
5.2. DESIGN PARAMETERS
2
Flux density (T)
1.5
1
0.5
0
0
2000
4000
6000
8000
Magnetic field in [A/m]
10000
Figure 5.2. Magnetic characteristics of M400 50A.
Stator tooth width
Stator yoke height
Rotor yoke height
Stator slot height
Airgap diameter
Magnet thickness
Stator slot wedge height
Number of poles
Number of stator slots
Magnet angle
Airgap length
Undercut angle
Stator slot opening
bts
hrs
hrr
hss
D
lm
hsw
p
Qs
α
δ
γ
bs0
Table 5.5. Independent parameters in machine geometry.
53
12000
CHAPTER 5. ANALYTICAL DESIGN OF PMSG
Figure 5.3. Typical geometry of an inner rotor surface mounted PMSG [21].
Maximum hot spot temperature
Ambient temperature
Permitted average temperature
120◦ C
20 ◦ C
70 ◦ C
Table 5.6. Nominal temperatures in the machine.
Connection type
Number of poles
Number of stator slots
Stator slot fill factor
Nominal line-line voltage
−
p
Qs
fs
−
Wye
64
72
0.5
400 V
Table 5.7. Winding parameters of the machine.
54
5.3. DESIGN PROCEDURE
Figure 5.4. Flowchart showing the optimisation procedure of PMSG.
5.3
Design Procedure
Figure 5.4 shows the flowchart followed for optimisation of PMSG. In the first
step, design requirements and constraints are introduced. In the next step, design parameters like characteristics of chosen material, winding parameters, etc are
introduced. In this step, still the design variables are not assigned any value.
Magnetic design is the first step after assigning the values to the airgap diameter
55
CHAPTER 5. ANALYTICAL DESIGN OF PMSG
Peak fundamental airgap flux density
Stator yoke flux density
Stator teeth flux density
Rotor yoke flux density
Current density
bδ (T )
B
b
Brs (T )
bts (T )
B
brr (T )
B
2)
b
J(A/mm
(0.2, 1.2)
(1.1, 1.5)
(1.5, 2.0)
(1.3, 1.6)
(3.0, 5.0)
Table 5.8. Design limitations suggested by J. Pyrhönen in [42].
and airgap flux density. The magnet thickness can be calculated by
Bm = Br,m
1
1 + µr lδme
(5.4)
where Bm is the maximum airgap flux density, Br,m is the remanence flux density
of the magnet at the working temperatures of the machine. µr is the relative
permeability of the magnet, δe is the effective airgap length and lm is the magnet
thickness. The stator and the rotor yoke height together with the stator tooth width
are determined, according to.
αBm D
(5.5)
hrs =
pkj Brs
αBm D
pkj Brr
(5.6)
αBm τs
2δ
(1 − )
kj Bts
D
(5.7)
hrr =
bts =
In these equations kj is the stacking factor and τs is the slot pitch. Table 5.8
includes design limitations of the flux density in various localities of the machine.
The slot geometry can be calculated in this step. Table 5.8 , moreover, includes
the limitations of the current density of a standard non salient pole synchronous
machine4 . This is to ensure safe thermal behaviour of the machine.
5.4
Design Objective
Electrical machines can be designed for different purposes, thus the optimisation
criterion will be different. Some of the criteria are presented below:
• torque per unit length
• efficiency
• weight/size
• cost
4
see Table 6.1 and Table 6.2 in [42] for more information
56
5.4. DESIGN OBJECTIVE
bδ
D/B
0.245 m
0.440 m
0.635 m
0.830 m
1.025 m
1.220 m
1.415 m
1.610 m
1.805 m
2.000 m
0.3 T
N/A
3.1
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.4 T
N/A
3.8
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.5 T
N/A
4.4
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.6 T
N/A
4.9
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.7 T
N/A
5.2
11.6
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.8 T
N/A
5.4
12.0
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.9 T
N/A
N/A
12.1
21.4
N/A
N/A
N/A
N/A
N/A
N/A
1.0 T
N/A
N/A
11.9
21.1
N/A
N/A
N/A
N/A
N/A
N/A
1.1 T
N/A
N/A
N/A
20.2
31.5
N/A
N/A
N/A
N/A
N/A
1.2 T
N/A
N/A
N/A
18.8
29.3
42.2
N/A
N/A
N/A
N/A
Table 5.9. Torque per unit length of considered machines in kNm.
The criterion torque per unit length has been used in the design of PMSG for this
purpose5 . Here it is assumed that other specifications like weight, size and cost will
be minimised. Various machines are investigated with respect to the fundamental
airgap flux density and the airgap diameter. Due to the violation of the restrictions
mentioned in Table 5.8 some combinations in the design are, therefore, excluded.
On the other hand, cost of active material, including permanent magnet, iron
and copper, is also one of the criteria in the current application. Considering cost
coefficient of active material 6 as
• cF E = 1 Euro/kg
• ccu = 8 Euro/kg
• cP M = 220 Euro/kg
The cost of active material for the machines shown in Table 5.9 is calculated and
given in Table 5.10.
The optimised machine for the highest torque per unit length is the one with
airgap diameter of 1.22 m and airgap flux density of 1.2 T . However this machine
is 12 times as expensive as the optimised machine for the lowest cost of active
material which has airgap diameter of 0.635 m and airgap flux density of 0.7 T . In
the following chapter results of simulation in a FEM software for the latter machine
are presented. 7
5
see Table 5.9
The given values are typical.
7
Usually a second run of optimisation is suggested. In the second run the optimised machine is
found for airgap diameters between 0.4400 m and 0.8300 m and airgap flux densities between 0.6
T and 0.8 T . The second run of optimisation led into a machine with total cost of active material
of 1.04 kEuro which is only 20 Euro cheaper than the chosen machine. This disregarded machine
had airgap diameters of 0.635 m and airgap flux density of 0.66 T .
6
57
CHAPTER 5. ANALYTICAL DESIGN OF PMSG
bδ
D/B
0.245 m
0.440 m
0.635 m
0.830 m
1.025 m
1.220 m
1.415 m
1.610 m
1.805 m
2.000 m
0.3 T
N/A
1.46
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.4 T
N/A
1.23
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.5 T
N/A
1.14
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.6 T
N/A
1.15
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.7 T
N/A
1.26
1.06
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.8 T
N/A
1.50
1.18
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.9 T
N/A
N/A
1.46
1.29
N/A
N/A
N/A
N/A
N/A
N/A
1.0 T
N/A
N/A
2.11
1.74
N/A
N/A
N/A
N/A
N/A
N/A
Table 5.10. Total cost of active material of considered machines in kEuro.
58
1.1 T
N/A
N/A
N/A
3.14
2.69
N/A
N/A
N/A
N/A
N/A
1.2 T
N/A
N/A
N/A
18.45
15.16
12.98
N/A
N/A
N/A
N/A
Chapter 6
FEM Simulation of PMSG
This chapter presents the FEM model of the optimised machine in Chapter 5.
The software used in the current work is Flux2D 10.4.1. In the first section, some
assumptions in the process of developing the FEM model are described. Further
electromagnetic characteristics of the optimised machine are given in section 6.2.
Last section shows the iron losses of the optimised machine. These iron losses are
used in thermal analysis in Chapter 7 .
6.1
Initial Considerations
This section treats some considered assumptions for the development of the
model in the software platform. It includes both technical and software aspects.
Geometry
– Due to the symmetry,
1
8
of the machine is modeled.
– Independent geometrical parameters as Table 5.5 are introduced to the
model. Figure 6.1 shows geometry of the optimised machine.
Mesh
– Mesh points are assigned as meshing tools. A parametric value is assigned
to the points in order to have 5/10 points in each line element. Figure
6.2 shows meshed geometry of the model.
Physics
– Stator and rotor iron are of laminated steel sheet with stacking factor of
0.96 .
– Magnetic characteristics of the magnet are modeled by the relative permeability and the remanence flux density. In other words it differs from
Figure 5.1 .
– A three-layer airgap is considered: One belonging to rotor mechanical set,
one belonging to stator mechanical set and the last one of compressible
air quality.
– An electrical circuit is made in Electriflux .
1
2
Electriflux is a trademark by Cedrat.
see Figure 6.3.
59
1 2
CHAPTER 6. FEM SIMULATION OF PMSG
Figure 6.1. Representation of the machine geometry in Flux2D.
Solver
– Flux2D, which is a two dimensional solver, is chosen for simulations.
3
– Study time limit is assigned to one electrical cycle with 50 points.
– Initial rotor position is set to 7mech.◦ . (see Figure 6.9 regarding finding
the value of initial rotor position.)
In Figure 6.3 Y-connection for the machine windings and the current sources is
presumed. The current sources, with sinusoidal currents, model the electrical system
connected to the machine. 4
6.2
Results of FEM Simulations
This section covers the simulation results in Flux2D model. Figure 6.4 illustrates
distribution of the iso value lines of the flux and the color shade of the flux density
at t = 1.25 × 10−3 sec at no load operation mode.
Figure 6.5a) shows induced voltage of the optimised machine in one electrical
cycle and Figure 6.5b) shows its harmonics spectrum. As seen from Figure 6.5b)
the back EMF spectrum shows very low harmonic contents. The peak fundamental
phase EMF is 251 V .
3
Due to the short length of the machine compared to its radius, three dimensional simulations
are suggested for future work.
4
Simulation with current sources containing Pulse Width Modulation (PWM) currents is suggested for future work.
60
6.2. RESULTS OF FEM SIMULATIONS
Figure 6.2.
elements.
Representation of the machine geometry in Flux2D with the mesh
Figure 6.3. The electric equivalent circuit applied to the FEM model.
61
CHAPTER 6. FEM SIMULATION OF PMSG
Figure 6.4. Iso value lines of the flux and color shade of the flux density at t =
1.25 × 10−3 sec at no load operation mode.
62
6.2. RESULTS OF FEM SIMULATIONS
Induced voltage
Harmonic spectrum of induced voltage
300
200
250
200
Voltage (V)
Voltage (V)
100
0
100
−100
50
−200
0
150
0.005
0.01
0.015
time (sec)
0.02
0
0
5
10
Harmonic orders
15
Figure 6.5. Induced phase voltage (phase A) a) Time variation of induced voltage
(left) b)Harmonic spectrum of induced voltage (right).
Figure 6.6 illustrates distribution of the iso value lines of flux and the color shade
of flux density at t = 1.25 × 10−3 sec at full load.
Figure 6.7a) shows no load airgap flux density at t = 1.25 × 10−3 sec and
Figure 6.8 shows its harmonics spectrum. As can be seen from the figure, the
no load airgap flux density spectrum shows very low harmonic contents. This is
strongly dependent on the pole and slot number combination5 . The peak value of
the fundamental no load airgap flux density is 0.74 T which is 4 % lower compared
to the expected value (0.77 T )6 . The sags in the waveform that can be observed
from Figure 6.7a) represents the permeance variation caused by the slot openings.
Their presence reduces the fundamental value. The order of harmonics with highest
peak value are the 5th and the 7th. Figure 6.7b) shows the airgap flux density at
nominal load. The peak fundamental value of the airgap flux density at nominal
load is 0.72 T . It can be noted from Figure 6.7b) , that there are some spikes,
these indicate a presence of the armature reaction caused by the currents in the
windings.
Figure 6.9 shows the torque of the optimised machine at DC current. The
torque is maximum at θ = 7 mech.◦ .
Figure 6.10 shows the cogging torque. 7 The peak to peak value of the torque
in Figure 6.10 is the absolute value of the cogging torque for the total machine
which is 17.5 N m . Figure 6.11 shows the torque at nominal load. The peak to
peak value of the torque in the bottom of Figure 6.11 is the absolute value of the
torque ripple for the total machine which is 56 N m . The mean value of the torque
is 1193 N m and it is 6 % lower compared with expected value (1273 N m ). The
5
see section 3.4.2.
After optimisation, the magnet thickness was increased a bit in order to ensure the mechanical
rigidity. Therefore, analytical value of the airgap flux density increased.
7
250 points is used in simulation of Figures 6.10 and 6.11 .
6
63
CHAPTER 6. FEM SIMULATION OF PMSG
Figure 6.6. Iso value lines of the flux and color shade of the flux density at t =
1.25 × 10−3 sec at full load operation mode.
64
6.2. RESULTS OF FEM SIMULATIONS
Full load airgap flux density
1
1
0.5
0.5
Airgap flux density (T)
Airgap flux density (T)
No load airgap flux density
0
−0.5
−1
0
−0.5
−1
0
10
20
30
40
Position (mechanical degree)
0
10
20
30
40
Position (mechanical degree)
Figure 6.7. Airgap flux density a) At no load (left) b) At full load (right).
Harmonic spectrum of no load airgap flux density
Airgap flux density (T)
0.8
0.6
0.4
0.2
0
−0.2
0
5
10
15
20
Harmonic orders
25
30
Figure 6.8. Harmonic spectrum of the no load airgap flux density.
DC current torque of the machine
1500
Torque (Nm)
1000
500
0
−500
−1000
−1500
2
4
6
8
Position (mechanical degree)
10
Figure 6.9. DC-current torque.
65
CHAPTER 6. FEM SIMULATION OF PMSG
Cogging Torque of the machine
10
Torque (Nm)
5
0
−5
−10
0
2
4
6
8
Position (mechanical degree)
10
12
Figure 6.10. The total cogging torque in the machine.
Torque (Nm)
Torque of the machine (full scale)
1000
500
0
0
2
4
2
4
6
8
10
12
Position (mechanical degree)
Torque of the machine (partial scale)
14
16
18
14
16
18
Torque (Nm)
1220
1200
1180
1160
0
6
8
10
12
Position (mechanical degree)
Figure 6.11. The total torque of the machine at nominal load (Full scale at the top
and partial scale at the bottom).
amount of the cogging torque is 1.5 % and the amount of torque ripple is 4.7 % .
6.3
Iron Losses
This section describes calculation of iron losses in stator and rotor lamination
in Flux2D. The Bertotti model is chosen in order to describe the iron losses in steel
sheets. Equation 6.1 shows the relation between different components of the iron
losses as a function of frequency and flux density. The electrical frequency is the
same in all locations in the iron, however the flux density is different8 . Iron losses
are given by equation
PF E = kh f B 2 +
8
3
σ
(πdF E f B)2 + 8.67 × kexcess (f B) 2
6
For introduction of different components of iron losses, see section 3.5.4.
66
(6.1)
6.3. IRON LOSSES
Hysteresis loss coefficient ( TW2sec
)
m3
1
Classical loss coefficient (conductivity) ( Ωm
)
W T 1.5
Excess loss coefficient ( m3 ( sec ) )
Thickness of lamination (m)
Stacking factor
Frequency (Hz)
kh
σ
kexcess
dF E
kj
f
59.23
723
4.05
0.0005
0.96
48
Table 6.1. Losses coefficients applied in FEM simulations.
x 10
Power Loss
Density (w/m/m/m)
4
4
Iron Loss Density
Fitted Curve
3
2
1
0
0
0.5
1
Applied Flux Density (T)
1.5
Figure 6.12. Fitted curve for iron loss density of M400 50A.
Iron
Iron
Iron
Iron
losses
losses
losses
losses
in
in
in
in
rotor in no load
stator in no load
rotor in nominal load
stator in nominal load
3W
117 W
9W
182 W
Table 6.2. Iron losses in rotor and stator of the optimised machine calculated in
FEM simulations.
where kh and kexcess are hysteresis and excess loss coefficients, dF E is the steel sheet
thickness and σ is the steel sheet conductivity. Table 6.1 shows the loss coefficients
considered in FEM simulations.
The first three parameters are calculated based on the curve fitting for given
iron loss density in the iron material datasheet 9 . Figure 6.12 shows the fitted curve
for iron loss density of M400 50A.
By introducing the loss coefficients to FEM models, the iron losses in stator and
rotor are calculated at no load and at nominal load conditions. These values, which
are later used in thermal analysis, are shown in Table 6.2 .
9
see appendix A
67
Chapter 7
Thermal Modeling of PMSG
Loss of energy cannot be avoided in electrical machines. It is created in different parts of the machine in the form of copper, iron and mechanical losses. These
losses have to be cooled away through dissipation of the heat: thus the thermal
constraints influence the rating of the machine. The problem that arises with temperature increase for example demagnetisation of the magnets in a PMSM. The
insulation material is very sensitive to temperature. Its lifetime reduces with higher
temperatures. Because of this the study on thermal behaviour of the machine is
performed. The iron losses calculated in section 6.3 are used here. This chapter
investigates the temperature rise in different parts of the machine by means of a
simplified lumped parameter model based on the model developed in [32].
7.1
Thermal Model
A lumped parameter model is employed to model the thermal behavior of the
machine. Similar to electrical circuit model, an equivalent thermal model including
thermal resistances is adopted. The nodes are chosen at interface between different
material or at loss generation points. Figure 7.1 shows chosen lumped parameter
model for thermal analysis. The nodes are chosen as
• Node 0: coolant.
• Node 1: frame.
• Node 2: stator iron.
• Node 3: coil sides of winding.
• Node 4: end windings.
Consequently, the model used in this chapter differs from the model in [32] in
these regards:
• The stator iron losses in yoke and teeth are aggregated.
69
CHAPTER 7. THERMAL MODELING OF PMSG
Figure 7.1. Lumped parameter thermal model consisting of an electric equivalent
circuit.
Loss type
Iron losses in stator
Copper losses in coil sides
Copper losses in end windings
value in W
182
342
272
Table 7.1. Losses in lumped parameter thermal model in Figure 7.1 .
• The rotor losses (iron losses and windage losses) and relevant thermal resistivities are neglected.
• The losses and thermal resistivity of magnets and bearings are neglected.
• Thermal capacitances of different materials are neglected. In other words a
steady state analysis is performed.
The ambient temperature is assumed to be 20◦ C .
Considered losses of the machine in the thermal analysis are given in Table 7.1.
The value of iron losses in the stator is calculated in section 6.3 by means of
simulation in Flux2D. Total copper losses at nominal load is
Pcu = 3Rcu I 2
√
I = 31.14/ 2 = 22.02 A
70
(7.1)
(7.2)
7.1. THERMAL MODEL
Thermal resistance
Rth1
Rth2
Rth3
Rth4
Rth5
value in ◦ C/W
2.4041 × 10−4
0.0058
0.0078
0.0150
0.0030
Table 7.2. Thermal resistances in Figure 7.1 .
where
Rcu =
1
ρcu ((pL + (D + hss )πkcoil )n2s q)
Acu
(7.3)
The resistivity of copper varies with temperature.
ρcu = (2 × 10−8 )(1 + 0.004 × (T − 20))
(7.4)
Since the temperature of winding is not known, the expected value could be used.
Considering class E , the hot spot temperature is expected to be lower than 70◦ C .
Then ρcu = 2.4 × 10−8 Ωm
The coil side copper losses and the end winding copper losses are distinguished
by
lF E
Pcu−cs =
Pcu
(7.5)
lav
Pcu−ew = (1 −
lF E
)Pcu
lav
(7.6)
The resistances in Figure 7.1 represents thermal resistivities according to:
• Rth1 : Thermal resistance between the frame and the coolant.
• Rth2 : Thermal resistance between the frame and the stator yoke.
• Rth3 : Thermal resistance between the stator yoke and the stator teeth.
• Rth4 : Thermal resistance between the stator teeth and the coil sides.
• Rth5 : Thermal resistance between the coil sides and the end winding.
They are calculated based on equivalent conductive and convective thermal resistances. They are in turn calculated based on geometry and thermal characteristics
of the machine. A Matlab code is developed in this regard and the results from
this code are presented here. Table 7.2 shows the values of thermal resistances in
Figure 7.1.
1
For introduction of symbols see "list of symbols and abbreviations".
71
CHAPTER 7. THERMAL MODELING OF PMSG
Parts of the machine
Frame
Stator
Coil sides
End winding
Value in ◦ C
20
31
40
41
Table 7.3. Temperature in different parts of the machine.
7.2
Steady State Analysis
Considering average coolant temperature as a reference, the temperature in each
node was computed. Table 7.3 shows the results. The hottest node in the machine
is the end winding. In reality the temperature can be few degrees more or less
in different locations in the end winding. The average temperature is much lower
compared with the permissible temperature (70◦ C). The major reason is very low
current density of 2.54 A/mm2 which results in low copper losses. If the current
density doubles, the copper losses increase by four times and the temperature rise
in the end winding increases drastically. Moreover, time harmonic losses of power
electronics converters are neglected in this analysis. Additionally, this model is a
simplification of 13 node model introduced by Lindström and for more accurate
results, it is suggested that a more advanced model is used. 2
2
For suggestions on future work, see chapter 8
72
Chapter 8
Conclusions and Further Work
8.1
Conclusions
In this work, a surface mounted, radial flux, inner rotor, longitudinal PMSG
with concentrated winding and natural air cooling is optimised with respect to the
cost of active material. Active material includes iron, copper and PM material.
Selection of topology is based on easy manufacturing process. For instance, to scale
up the machine for three times higher torque rating, the length of the machine can
be increased by three times and a new design can be avoided. The optimisation
objective function is set to minimise the cost of active material. Total active weight
of the machine is limited to approximately 110 kg. From the requirements, the
size limit on outer diameter of the machine is met by far. The shaft diameter is
higher than the minimum permitted value 1 which represents mechanical continuous
operation despite the high torque density. A FEM model is developed in Flux2D
and the performance is verified. Results from FEM analysis show low harmonic
contents in the induced voltage and the airgap flux density. Also by employing
a concentrated winding a high winding factor of 0.945 is achieved. The torque
ripple and the cogging torque are very low (respectively 4.7 % and 1.5 %) and the
cogging torque agrees very closely with corresponding constraint (around 1 %). The
efficiency is 93.4 % at nominal load (magneto-static analysis) and it agrees with the
value required by the application(94 %). The machine enjoys from low temperature
rise which serves the purpose of very long lifetime well.
8.2
Further Work
Various tasks can be conducted based on the present design. The list below
encloses the most interesting ones.
• 3D FEM analysis: The simulation software in this task has been Flux2D. In
two dimension simulations, effect of end windings on electromagnetic analysis
1
see Table 5.1
73
CHAPTER 8. CONCLUSIONS AND FURTHER WORK
is presumed to be negligible. However, length of the optimised machine is
much shorter than its radius. Therefore, presence of end windings on quantities like inductances can be pronounced. Hence, it is suggested that a three
dimension FEM analysis is taken to ensure a good performance.
• Time harmonics: In the electrical modeling of FEM analysis, the load connected to the machine terminals are modeled by sinusoidal current sources.
However, the machine is connected to the load/grid via converters. This
means that time harmonics will be injected into the machine. Therefore, it
is suggested that in the electrical modeling of FEM analysis, current sources
including harmonics are introduced.
• Control method: Control method of the optimised machine is left out of the
scope of the present work. However, it will be tremendous to investigate
an appropriate control method. The decision, first, can be made between
the methods which either include or exclude wind speed measurement2 . The
chosen control method can, moreover, influence time harmonics introduced in
the previous item.
• Wind analysis: Optimised machine’s performance is modeled only at full load
operation mode. One of the reasons is that this ensures that the machine will
always work in safe thermal behavior. However, the wind speed and direction
is consistently varying, which makes the machine to work at loads lower than
nominal load, and changes its direction of rotation frequently. It will be
interesting to model the machine performance in realistic wind conditions.
For instance, depending on site mean wind speed3 , it might be possible to
increase the amount of copper in the machine.
• Advanced thermal analysis: The thermal model developed in this work is a
simplification of the model introduced in [32] by Lindström. The assumptions applied in this model are mentioned in section 7.1. It is recommended
that an advanced thermal modeling is conducted to observe a more accurate
temperature pattern.
• Flux weakening capability: In the present work, base speed of the machine is
assumed to be very close to the maximum permitted speed. Thus, a "constant
power speed range" is not aimed at this work. However, it would be interesting
to consider the field weakening capability at the design stage. This requires a
more accurate model of wind turbine torque speed diagram. When it comes
to control of the machine, it is suggested that the torque trajectory of the
wind turbine and the generator intersect each other in generator’s base speed.
In other words, the wind turbine and the generator should have the same size.
2
3
For a brief introduction of control methods, see section 2.4.2
which is supposedly less than nominal speed
74
8.2. FURTHER WORK
• Building a prototype: This work has focused on optimisation of a PMSG and
verifying its electromagnetic and thermal performance via FEM and lumped
parameter modeling, respectively. The models have authenticated that the
machine works according to the expectations. The next step in this regard is
building a prototype based on the proposed machine in this work. The advantages of validation of prototype performance are of practical and scientific
type:
1. Investigation for cost reduction: The present model of the machine addresses efficiency as high as 94 % and very low temperature rise. If
these outstanding qualities are confirmed by measurements results, they
open the way for making some more compromise between cost and performance. For instance, one possibility can be to replace copper with
aluminum in the same design. This results in lighter weight and lower
cost of the machine. On the other hand, it will decrease the efficiency
and will increase temperature rise. The tradeoff can be fulfilled, if the
advantages outweigh the disadvantages.
2. Control method implementation: The feasibility of a control method can
be verified by means of testing the prototype together with a controller.
75
Appendix A
Datasheet of M400 50A by
Surahammar Bruk AB
77
APPENDIX A. DATASHEET OF M400 50A BY SURAHAMMAR BRUK AB
Figure A.1. Datasheet of M400 50A by Surahammar Bruk AB.
78
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[31] G. Kylander. Thermal modelling of small cage induction motors. PhD thesis,
Chalmers Univ. Technol., Gothenburg, Sweden, 1995.
[32] J. Lindström. Development of an experimental permanent magnet motor drive.
Lic. thesis, Chalmers Univ. Technol., Gothenburg, Sweden, 1999.
[33] D. Svechkarenko. Thermal modeling and measurements of permanent magnet
machines. Master’s thesis, Royal Inst. of Tech., Sweden, 2004.
[34] R. Bonert C. Mi, G. R. Slemon. Modeling of iron losses of permanent magnet
synchronous motors. In IEEE trans. on Inductrial Applications, volume 39,
2003.
[35] F. Sahin. Design and development of a high speed axial flux permanent magnet
machine. PhD thesis, Eindhoven Univ. of Tech., The Netherlands, 2001.
[36] G. McPherson and R. D. Laramore. An Introduction to Electrical Machines
and Transformers. Canada: John Wiley and Sons Inc, 2 edition, 1990.
[37] L. H. Hansen A. D. Hansen. Market penetration of wind turbine concepts over
the years. Technical report, Riso National Lab. Roskilde, Denmark, 2008.
[38] N. Smith. Motors as Generators For Micro-Hydro Power. UK: Russel Press
Ltd, 2 edition, 1997.
[39] P. K. Goel S. S. Murthy, B. Singh and S. K. Tiwari. A comparative study
of fixed speed and variable speed wind energy conversion systems feeding the
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1 edition, 1990.
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[41] V. Kinnares B. Sawetsakulanond. Design, analysis, and construction of a small
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List of Tables
Different classes of an insulation material due to IEC − 85. . . . . . . .
35
Design requirements and constraints. . . . . . . . . . . . . . . . . . . . .
Mechanical parameters involved in determination of minimum shaft diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Characteristics of VACODYM 655 AP. . . . . . . . . . . . . . . . . . . .
5.4 Characteristics of M400 50A. . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Independent parameters in machine geometry. . . . . . . . . . . . . . . .
5.6 Nominal temperatures in the machine. . . . . . . . . . . . . . . . . . . .
5.7 Winding parameters of the machine. . . . . . . . . . . . . . . . . . . . .
5.8 Design limitations suggested by J. Pyrhönen in [42]. . . . . . . . . . . .
5.9 Torque per unit length of considered machines in kNm. . . . . . . . . .
5.10 Total cost of active material of considered machines in kEuro. . . . . . .
49
3.1
5.1
5.2
6.1
6.2
7.1
7.2
7.3
50
51
52
53
54
54
56
57
58
Losses coefficients applied in FEM simulations. . . . . . . . . . . . . . .
Iron losses in rotor and stator of the optimised machine calculated in
FEM simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
Losses in lumped parameter thermal model in Figure 7.1 . . . . . . . .
Thermal resistances in Figure 7.1 . . . . . . . . . . . . . . . . . . . . . .
Temperature in different parts of the machine. . . . . . . . . . . . . . .
70
71
72
82
67
List of Figures
List of Figures
1.1
1.2
Annual capital investment in new renewable energies between 2004 and
2009 in US Dollars [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Renewable energy share of global energy consumption by 2008 [1]. . . .
1
2
2.1
2.2
2.3
2.4
Power coefficient versus tip speed ratio [3]. . . . . . . .
An H rotor VAWT [3]. . . . . . . . . . . . . . . . . . . .
A 450 kw HAWT with 37 m rotor diameter (Bonus) [2].
Horizontal plan of a VAWT [5]. . . . . . . . . . . . . . .
6
8
9
9
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3.1
Block diagram of a fixed speed wind energy system including a conventional SCIG, a gearbox and a transformer [2]. . . . . . . . . . . . . . . .
3.2 Block diagram of a typical DFIG including a transformer [2]. . . . . . .
3.3 Cross sectional view in radial direction and in axial direction, respectively, of a typical radial flux PMSG [21]. . . . . . . . . . . . . . . . . .
3.4 Cross sectional view in radial direction and in axial direction, respectively, of a typical axial flux PMSG [21]. . . . . . . . . . . . . . . . . . .
3.5 Fraction of a typical transversal flux PMSG [22]. . . . . . . . . . . . . .
3.6 Inner rotor PMSG (left) and an outer rotor PMSG (right) [26]. . . . . .
3.7 A surface mounted rotor for a PMSG [15]. . . . . . . . . . . . . . . . . .
3.8 Two different inset magnet rotors for PMSGs [15]. . . . . . . . . . . . .
3.9 Six different buried magnet rotors for PMSGs [15]. . . . . . . . . . . . .
3.10 Cross section of a pole pair of a V shaped buried magnet design (left)
and a tangentially buried magnet design (right) [21]. . . . . . . . . . . .
3.11 Windings in low speed PMSG a) distributed overlapping winding. b)
concentrated overlapping winding. c) double layer concentrated nonoverlapping winding. d) single layer concentrated non-overlapping winding [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 A typical magnet characteristics curve [20]. . . . . . . . . . . . . . . . .
4.1
4.2
Time variation of market share of yearly installed power of fixed speed
WECS (including induction generator, capacitor banks, soft starter and
output transformer) [37]. . . . . . . . . . . . . . . . . . . . . . . . . . .
The operating zones of induction machine [41]. . . . . . . . . . . . . . .
83
21
22
25
26
27
28
28
29
30
31
32
36
44
47
List of Figures
5.1
5.2
5.3
5.4
Magnetic characteristics of VACODYM 655 AP. . . . . . . . . .
Magnetic characteristics of M400 50A. . . . . . . . . . . . . . . .
Typical geometry of an inner rotor surface mounted PMSG [21].
Flowchart showing the optimisation procedure of PMSG. . . . .
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6.1
6.2
6.3
6.4
Representation of the machine geometry in Flux2D. . . . . . . . . . . .
Representation of the machine geometry in Flux2D with the mesh elements.
The electric equivalent circuit applied to the FEM model. . . . . . . . .
Iso value lines of the flux and color shade of the flux density at t =
1.25 × 10−3 sec at no load operation mode. . . . . . . . . . . . . . . . .
6.5 Induced phase voltage (phase A) a) Time variation of induced voltage
(left) b)Harmonic spectrum of induced voltage (right). . . . . . . . . .
6.6 Iso value lines of the flux and color shade of the flux density at t =
1.25 × 10−3 sec at full load operation mode. . . . . . . . . . . . . . . . .
6.7 Airgap flux density a) At no load (left) b) At full load (right). . . . . .
6.8 Harmonic spectrum of the no load airgap flux density. . . . . . . . . . .
6.9 DC-current torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 The total cogging torque in the machine. . . . . . . . . . . . . . . . . .
6.11 The total torque of the machine at nominal load (Full scale at the top
and partial scale at the bottom). . . . . . . . . . . . . . . . . . . . . . .
6.12 Fitted curve for iron loss density of M400 50A. . . . . . . . . . . . . . .
7.1
52
53
54
55
60
61
61
62
63
64
65
65
65
66
66
67
Lumped parameter thermal model consisting of an electric equivalent
circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
A.1 Datasheet of M400 50A by Surahammar Bruk AB. . . . . . . . . . . . .
78
84